Tantalum capacitors possess very low electrical leakage, (high leakage resistance), and will retain a charge for a long duration, they are also more tolerant of harsh, hot operating environments unlike standard aluminium electrolytic capacitors. Tantalum capacitors are relatively expensive, particularly the military grades, they are not particularly tolerant of heavy charge and discharge currents, particularly of a repetitive nature and their effective series resistance, ESR, is quite high when compared to aluminium electrolytics. As with all electrolytic capacitors, correct polarity must be observed otherwise the capacitor will depolarize and the dielectric oxide layer will be reduced back to the metal, reducing the resistance of the device and causing it to become very hot and possibly explode. Tantalum capacitors are less prone to "drying out", causing a decrease in capacitance as is often the case with aluminium electrolytic capacitors particularly when used in hot environments. They maintain their designed capacitance under such conditions over long periods of time, (decades).
In some low-power, battery-operated systems, a tantalum capacitor may be the cause of excessive current. The usual suspect is ESD damage to a CMOS device.
However there have been several recent cases where a plastic encapsulated, surface mounted, tantalum capacitor was the source of the excessive current.