Flush mountable latches and locks for industrial cabinets, tool carts, electrical equipment enclosures and the like utilize versatile housings together with a variety of types of handles that are movable relative to the housings to effect unlatching movements of spring-biased, pivotally mounted latch bolts, with pivotally mounted operating arms serving to drivingly interconnect the handles with the latch bolts. Lockable embodiments have locking mechanisms that prevent operating movements of the operating arms, but do not prevent pivotal movement of the latch bolts out of their latched positions, whereby even the lockable embodiments have latch bolts that can be "slammed" into latching engagement with suitably configured strike formations. Other improvement features reside in the provision of coaxially-pivoted overlying sets of latch bolt and operating arm components that cooperate in a plurality of ways, and in the provision of stop formations, torsion-spring-receiving formations, and co-acting drive formations, with such features enabling the resulting latch and lock assemblies to employ a small number of relatively movable parts that can be assembled, installed and serviced with ease.