My interest on random allocations is not recent, and was revived in the last years by the need for analyzing some random generation algorithms, for which "waiting-time models" turned out to be well-suited:
Older results deal with identifying classes of models (often related to database modelization, or to a learning problem) that are amenable to a uniform treatment. They often lead to so-called "occupancy urn models", i.e. models where a set of balls are thrown into a sequence of urns and the question is, e.g., the distribution of the number of empty urns. Some of these results are static, some are « semi-dynamic » in the sense that queries and insertions, but not deletions, are allowed, and some are fully dynamic and allow for deletions.