Quantitative genetics is the study of continuous characters.
Our study of living things requires us to make observations and measurements of features that we find interesting. There is, arguably, an infinite number of features, or characters, that I can arbitrarily choose to measure of an organism. Such features can be categorized into being meristic or continuous characters. Meristic characters are measured as being in one of several discrete states. For example, a character can be scored as being present or absent, or being in one of several states: e.g. whether peas are smooth or wrinkled. Often, an integer value is assigned to each state. On the other hand, an infinite number of states can be assigned to a continuous character because it is measured by some value on the line of real numbers. You cannot be completely accurate about how tall you are because there is always another significant digit, and so your height is a continuous character.
Some meristic characters have a Mendelian pattern of inheritance. Gregor Mendel was fortunate enough to obtain such characters in a well-behaved genetic system, and observed that mating the offspring of a hybrid cross regenerated parental characters that had disappeared. It was as if it were genetic particles being inherited that could suppress one another's expression. Of course, we now know that this particulate mode of inheritance was symptomatic of a single gene being the basis of a meristic character. Many biologists at the time believed that most characters could be demonstrated to be Mendelian. Unfortunately, most characters are generated by the expression of many genes -- they are "polygenic".
The study of QTLs: How many genes?
Unlike Mendelian genetics, quantitative genetics attempts to understand the polygenic basis of continuous characters. This is very difficult, and in fact for a long time biologists didn't believe that continuous characters even had a particulate mode of inheritance at all. Quantitative genetics really didn't get started until Yule and R.A. Fisher pointed out that several Mendelian genes acting together could produce an apparently continuous distribution of characters. Once this hurdle was cleared, however, many interesting questions could be asked: How many genes are influencing a character? Are there an important few, or are many equally important? How are these genes passed from one generation to another? How do they respond to natural selection?
Before the onset of molecular genetics and the development of gene sequencing, biologists had to be very clever in deciphering the genetic basis of continuous characters. Elegant breeding experiments were developed in conjunction with equally elegant mathematical models and statistical methods. For example, consider two inbred populations of fruit flies. Individuals belonging to the same inbred population can be expected to be nearly genetically identical -- put another way, you would expect to find similar alleles at most genes. Taking two such populations that have converged on two different genetic states and performing crosses between them will create a genetically homogeneous population of heterozygotes. In the classic genetic literature, you will find this refered to as the "F1" population, where 'F' is an abbreviation for "filial" (a rather archaic synonym for offspring). No information is gained about the number and kind of genes underlying a particular character here; at least not until we have performed further crosses from this new heterozygous population. Crosses between flies of the F1 population create a population of reassortants and recombinants. This population, unlike its ancestors, is not genetically homogeneous because each individual is a random collection of alleles chosen from the two possible at each gene. This is the F2 population.
This method of crossing inbred populations was the bread and butter of experimental quantitative genetics who could obtain an estimate the number of genes underlying a continuous character. For brevity's sake, I'll start using the more conventional term for these genes: quantitative trait loci, or QTLs. I won't go into the statistical analysis of the distribution of the character in the F2 population, but interested souls should look up references on the Wright-Castle estimator. Perhaps an intuitive explanation would be a good subject for a subsequent write-up...
The study of the number and kinds of QTLs has recently become a sophisticated sub-discipline incorporating genomic data and computionally-intensive statistical methods. Although many issues are still unresolved, enough information has been accumulated to draw certain conclusions. It appears that there are few genes with large effects on a continuous character, and many genes with comparably small effects. Pleiotropy, or the extended effect of a single gene on more than one character, appears to be pervasive. With complete genomes for several species available, greater questions have become accessible: can we predict where QTLs will be found in the genome, or is there neither rhyme nor reason to their distribution? Where do QTLs come from?
Explaining variation: why so many forms?
Another endeavour undertaken by the discipline was to explain why there was so much genetic variation in the wild. Such an abundance had long since been demonstrated by the efforts of breeders on domesticated species. If the demands set by the environment were constant, why would an adapted population harbor genetically deviant types? Moreover, could quantitative genetics provide a sound and useful genetic explanation? Again, the approach took both experimental and theoretical efforts. Characters were decomposed into having genetic and environmental determinants (as well as a third component to accomodate interactions between the two). The genetic basis of character variation could further be split between additive and non-additive sources. In short, it begins to resemble a multivariate regression model; indeed, I rather suspect that much development of the mathematics of linear analysis owes much to the study of biological continuous characters. Experimentally, the genetic and environmental determinants of variation were accessible by nested breeding designs. For example, a completely inbred population would expect to display variation solely caused by the environment.
For further reference:
DS Falconer and T Mackay. Introduction to Quantitative Genetics.
M Lynch and B Walsh. Genetics and Analysis of Quantitative Traits.
NH Barton and M Turelli. 1989. Evolutionary Quantitative Genetics: How little do we know? Annual Review of Genetics 23: 337-70.