When people think of the Roman Empire, they generally imagine a combination of hegemonic military prowess, debauched excess on the part of an aloof and unaware upper class, and vicious court intrigues on the part of men and women alike to curry favor with or advance to become antiquity's version of the Leader of the Free World - the Emperor himself. While none of these assumptions is fundamentally incorrect, after a certain point in time, it was definitely more of the second and third than the first. For the time when all three notions were accurate, however, the leading personalities of the state were clustered around the Julio-Claudian Dynasty, comprised of two of Rome's most powerful families: the Julians and the Claudians (specifically the Nerones branch so named because of their inherited cognomen "Nero"). The Julians were relative newcomers to the political scene whereas the Claudians had been prominent in Roman politics since the inception of the Roman Republic in the sixth century BC. One of the most prominent Claudians in the early Empire was Julius Caesar Drusus, more properly known as Nero Claudius Drusus or colloquially as Castor. Drusus was the only natural son of Tiberius, the second Roman Emperor.
Drusus was born in 13 BC to Tiberius and Vipsania Agrippina, an impeccable pedigree for the time: his father was the son of Livia, the wife of the Emperor Augustus, and his mother was the daughter of the famed general and lifetime friend and ally of Augustus, Marcus Vipsanius Agrippa. He was named after his uncle, Drusus Claudius Nero Germanicus, in violation of the standard Roman naming convention of an eldest son being named after his father; confusingly, multiple sons were often given the same name and differentiated by their respective cognomina (for example, two later Emperors had been brothers but both had been named after their father). Tiberius was returning the favor as his brother, the elder Drusus, had named his first son after him in a similar (but frankly non-controversial) contravention of normality.
If there's one thing to take away from this, it's that the Julio-Claudians were a very tight-knit group but that the separate branches were even more insulated from one another. One of the reasons for this was that, almost up until his death, Augustus had no clear successor. Augustus had only had one child, a daughter named Julia, as a result of his marriage to Scribonia in 39 BC. Augustus and Livia had only ever conceived one child, but the latter miscarried and no further attempts seem to have been made on their behalf to have more. Augustus' life was essentially one debilitating illness after another, so it was clear to him in the late 20s BC that it would make sense to have someone in place to step in and assume power in the event of his death. He had a strong preference for a Julian; his first choice was his nephew, Marcus Claudius Marcellus (who was both a Julian and a Claudian), to whom he gave his daughter Julia in marriage. Marcellus died in 23 BC of unknown causes. His next choice was his longtime friend Agrippa (the most qualified man in the Empire for the job), and he too was married to Julia after Marcellus' death. Julia and Agrippa had several children, including three boys. Agrippa died in 12 BC, though, so Augustus cultivated his grandsons Lucius and Gaius, going so far as to adopt them as his own sons. Livia, however, had a strong and altogether natural desire to see her elder son (by her pre-Augustus marriage) Tiberius succeed her husband. Augustus was not dismissive of this out of hand, but he did not get along with Tiberius on a personal level; still, he yet again used his daughter to cement an alliance and forced Tiberius to divorce Vipsania and marry Julia just in case. The marriage was miserable and their only child died so young that its name and gender are lost to us. It ended when Julia's infidelity to Tiberius was made publicly known and Augustus banished his daughter from Rome for bringing shame upon him (he was an active promoter of "family values" in public policy). By 4 AD, both Lucius and Gaius were dead from unusual causes. Augustus finally adopted Tiberius as his heir, but as a condition of this, he required Tiberius to disavow his own son Drusus in favor of his nephew (who had been named after him) Tiberius Claudius Nero Germanicus (a preferable candidate to Augustus because Germanicus was a blood relative; his sister Octavia was Germanicus' grandmother). He reluctantly did this and both men were adopted into the Julian clan.
Despite this seeming side-lining, however, Augustus appointed Drusus to various offices and military commands. He showed promise both politically and militarily and, significantly, had been allowed to marry into the Julian family. His wife, Livilla (or sometimes Livia Julia), was the sister of Germanicus, making them first cousins. Livilla had previously been married to Gaius Caesar, one of Augustus' earlier preferred successors, so it's clear that while Drusus was not Augustus' first choice for an heir, he might be allowed to father a future Emperor. Indeed, Drusus and Livilla had twin boys in 19 (though only one, Tiberius Gemellus, survived infancy).
When Augustus died in 14 AD, Tiberius succeeded him. Germanicus died in highly supsicious and controversial circumstances in 19. It was immediately assumed that Tiberius had had a hand in his adopted son's death, but this was impossible to prove then just as it is now. What is certain, however, is the fact that for as unpopular as Tiberius was, Germanicus was even more beloved by the people of Rome and whether the accusations of complicity were true or not, the latter's death did nothing to help Tiberius' cause. Tiberius readopted his natural son Drusus into the Julian family and his name then became Julius Caesar Drusus, which he seems to have preferred to his birth name. As the heir apparent to the highest office in Rome, Drusus' power and influence greatly increased. He had already been consul in the year 15 and was governor of Illyricum for about three years after that.
While things were looking up for Drusus, he did have a few problems on his hands. He was known in Imperial circles to be a heavy drinker and was frequently driven to extreme anger by the slightest perceived insults. This irascibility brought him into conflict with his father's most important minister, Lucius Aelius Seianus, commonly known in English as Sejanus. Sejanus was the commanding officer of the Praetorian Guards and had been among the first to pledge his loyalty to Tiberius upon Augustus' death. Drusus did not care for Sejanus, viewing him as a social inferior: he had been born an equestrian, while Drusus was a patrician (ironically, Augustus was an equestrian as well). More significantly, however, Sejanus was intensely jealous of Drusus' power: the latter was consul for the year 21 with Tiberius and was granted the tribunician power (which was the same office Augustus had given Agrippa during an illness he did not expect to survive, meaning that it was the primary legal basis for the Emperor's authority) the following year. The writing was on the wall: Drusus would succeed Tiberius upon his father's death and/or resignation.
In 23, though, everything changed following an argument between Sejanus and Drusus, which resulted in the latter physically striking the former. Sejanus and Drusus had had personal issues going back to at least 15 when both men were sent to put down a legionary revolt in Pannonia and argued over strategy. Although Drusus was given offices and powers commensurate with his status as heir apparent to the Empire, it was Sejanus upon whom Tiberius implicitly relied for advice and to get things done; needless to say, both men resented this arrangement. In addition to being rivals for the throne, Drusus and Sejanus were also rivals in love, although Drusus was not aware of this: Livilla had been infatuated with Sejanus for years and the two had been carrying on an affair since at least 19. Sejanus and Livilla concocted a plot to kill Drusus based on a systematic but subtle poisoning regimen. Drusus fell ill and died much the same way as Germanicus had. Tiberius was of course devastated, but suspected no foul play. After his son's death, he gradually came to lose interest in statecraft and government, which eventually caused him to abandon Rome in 26 for his pleasure dome on the island of Capri. Sejanus became the de facto ruler of the Roman Empire at this point since Tiberius could not be bothered to care about his duties.
As sort of an epilogue, the people of Rome seem not to have mourned Drusus too deeply at the time of his death, although they would during Sejanus' semi-regency and indeed moreso after the ascension of Tiberius' eventual successor. Sejanus embarked on a reign of terror that saw massive proscriptions throughout Rome and had everyone of slightly decent means fearing for his life (since most of the people killed during this time were done so for the purpose of confiscating their wealth). Sejanus and Livilla convinced Tiberius to approve the murder of Germanicus' male children Drusus and Nero as well as his widow Agrippina, claiming they were part of a plot to dethrone him; really, Sejanus was just concerned that any blood relatives of Tiberius would threaten his position. Though Tiberius relied on Sejanus to an extent far out of proportion with his value as an administrator and as a human being, he refused him the honor of Livilla's hand in marriage (though they were still involved). In the year 31, though, Tiberius decided that Sejanus was getting too big for his britches. So naturally, he made Sejanus his colleague as consul and agreed to let him marry Livilla. He then set out on a bizarre but effective campaign to undermine Sejanus' position, which included bringing up the only surviving son of Germanicus, Gaius, to a significant public office and soundly condemning some of Sejanus' most important associates. Nobody, least of all Sejanus, knew what to make of all this until 31 when Tiberius sent a letter to Sejanus, telling him of his intention to grant him the tribunician power during a special session of the Senate. Upon his arrival, however, Sejanus was greeted with another letter from Tiberius condemning him to death. Sejanus was executed and his corpse was torn apart by a mob. He was given a damnatio memoriae and not long afterwards, Tiberius became aware of Sejanus' complicity in his son's death. He had Sejanus' surviving family killed and had his niece Livilla starved to death. Tiberius finally announced that his successors would be Drusus' son Gemellus and Germanicus' son Gaius, both of whom were considered too young to be as conniving as Sejanus had been. Popular enthusiasm favored Gaius far more than Gemellus since Drusus had never really been that beloved by the citizenry (though to be fair, they did not loathe him either). Tiberius died in 37 and Gaius was seen as his primary successor, to the detriment of Gemellus. Gaius had Gemellus executed in early 38 on the false assertion that he had attempted to kill him. Gaius, naturally, is more famously known to us as Caligula, and his reign definitely made the Roman people miss Drusus.