There is a good review article in this month's NEJM entitled "Use of Diuretics in Patients with Hypertension" by Ernst and Moser which focuses predominantly on the thiazide class of diuretics. The thiazides are considered a FUNCTIONAL rather than a STRUCTURAL class of medications--that is, not all compounds considered thiazides have the same chemical backbone, but rather they are classified as such based on their common ability to inhibit the sodium-chloride electroneutral transporter in the distal convoluted tubule. The NEJM article breaks down thiazide diuretics into "thiazide-type" diuretics (which are structurally similar, containing a benzothiadiazine group--these include HCTZ and chlorothiazide, for instance) and the "thiazide-like" diuretics (which do not have the benzothiadiazine group--these include chlorthalidone, metolazone, and indapamide).
The hypertension lowering properties of thiazides occur via two mechanisms: an early anti-hypertensive effect is observed as a result of volume depletion, while long-term benefits on blood pressure appear to be due to decreasing vascular resistance, via a mechanism which is not entirely clear.
A few other tidbits about specific thiazide diuretics which may be useful clinically: the half-life of HCTZ is only 9-10 hours; thus, if you really want to inhibit Na reabsorption in the distal nephron it is necessary to dose bid (the traditionally anti-hypertensive dosing is typically given just once daily). Chlorthalidone is unique amongst the thiazides in that it has a very long half-life which enables once daily dosing. Most thiazide diuretics tend to markedly decrease in efficacy at low GFR's (e.g., less than 40 ml/min), though the article states that metolazone is more resistant to this effect than other thiazides, explaining its occasional utility in the diuresis of individuals with the cardiorenal syndrome.
Side effects of thiazide diuretics include hypokalemia, hypovolemia (e.g., orthostatic hypotension), gout flares, a small but measurable increased susceptibility to the development of diabetes mellitus, and rarely causing an allergic reaction to individuals with a severe sulfa allergy.