Maximal Clique Enumeration (MCE) is a fundamental graph mining problem, and is useful as a primitive in identifying dense structures in a graph. Due to the high computational cost of MCE, parallel methods are imperative for dealing with large graphs. We present shared-memory parallel algorithms for MCE, with the following properties: (1) the parallel algorithms are provably work-efficient relative to a state-of-the-art sequential algorithm (2) the algorithms have a provably small parallel depth, showing they can scale to a large number of processors, and (3) our implementations on a multicore machine show good speedup and scaling behavior with increasing number of cores, and are substantially faster than prior shared-memory parallel algorithms for MCE; for instance, on certain input graphs, while prior works either ran out of memory or did not complete in 5 hours, our implementation finished within a minute using 32 cores. We also present work-efficient parallel algorithms for maintaining the set of all maximal cliques in a dynamic graph that is changing through the addition of edges.