Specific voltages*
Continuity
Resistance
Frequency
Capacitance
*I prefer a solenoid tester for most testing and troubleshooting, because most VOM's have a high input impedance. They present very little loading to the circuit under test, and often indicate voltage where there is none (useable.)
Voltage is induced in conductors in close proximity to other, current-carrying conductors. A solenoid tester requires 'real power' to indicate, because of its relatively low impedance, and doesn't respond to small induced voltage.