Solid tantalum capacitors have a lot of advantages: very low inductance in surface mount packages, ESR low but not so low that your LDO regulators start oscillating; and good capacitance per unit volume. Unfortunately they're also prone to burn up when mistreated, which makes many engineers wary of them. This war story, entitled What a Cap-astrophe! talks about how to treat them properly, and how a bit of TLC after soldering can restore their full performance.