Of all the starships familiar to fans of the Star Trek series, the Miranda Class is one of the most recognizable - the Reliant from Star Trek II: The Wrath of Khan was of the Miranda Class. That being said, there's quite a lot about its history we don't know. For the purposes of this writeup, I'm assuming that only the movies and the various series and what can be inferred from them are canon - the books, video games, rpgs and such are being ignored - they tend to only muddy the issue anyway.
The Miranda Class spaceframe is the oldest still in active service, probably due to its cheap production costs and fast production rates. Star Trek II was the first appearance of this class of starship. The introduction of a new class of ship in the movie was a practical one - since it was going to spend most of its screen time hunting the Enterprise, the two ships had to be visually distinct so people wouldn't get confused over who was kicking whose butt. Since then, Miranda Class starships have made appearances in Next Gen and DS9, usually as couriers, cannon fodder or relics from the past. Miranda class variants (such as Sisko's old ship, the USS Saratoga) are sufficiently modified from their initial spaceframes to be thought of as a separate class, usually through the addition of shuttle landing platforms, outboard sensor systems (or HUGE guns, depending on who you ask) and through the elimination of the roll bar.
The Miranda class is designated as a heavy frigate/light cruiser due to its lack of a secondary hull - powerplant and engineering sections are housed in an elongated area at the back of the primary hull (it seems silly to call it the 'saucer', as it isn't one) along with two massive shuttlebays. While making construction simpler, the lack of a secondary hull necessitated a smaller warp reactor - range is therefore far more limited than that of its big brother. The warp nacelles are underslung, connected to the bottom of the primary hull with pylons. These pylons extend over the engineering hull and are joined by a roll bar (well? What would you call it?) containing a sensor and torpedo pod. Information on the class' deflector systems is not available, but I'm guessing it's not all that powerful as miranda class starships lack a standard deflector dish.
Put simply, Miranda class starships are over-weaponed for a ship of their size, a fact leveled by their top-heavy nature and smaller than usual powerplant. Apart from the standard twelve phaser cannon arranged in pairs along the dorsal and ventral surfaces of the primary hull, a megaphaser cannon resides at each lateral end of the roll bar and four torpedo launchers (two fore, two aft) are contained in the pod on the ships' back. All well and good in two dimensional space, but the class is horribly outmatched from below - neither the torpedos nor megaphaser cannon can be brought to bear on attackers approaching on the -z axis (though to be fair it should be noted that Constitution class starships ( the Enterprise, et al.) are at a horrible disadvantage if attacked from the rear - nobody's perfect.)
Various refits have been proposed by fans (though never seen) that rectify this situation by mirroring the upper cannons with a similar pair below the primary hull, but generally add a small secondary hull to feed power to them and, usually, a third warp nacelle for good measure. These modifications are so similar to the fabled Dreadnought Class starship that any real comparison between them and the miranda class is an exercise of the imagination.
Miranda's a workhorse designed to fill the gaps between her sister ships - light and fast with reduced range and impressive hanger capabilities, she resembles an interceptor or patrol ship on steroids, a fact that most likely has much to do with her 80+ year service to Starfleet.