I will go over some of my past and present work on hashing-based data structures.  After presenting some background on Bloom filters and cuckoo hashing, we will describe cuckoo filters, an efficient data structure for approximate set membership that improves on the well-known Bloom filter. We then discuss recent work on how to make cuckoo filters adaptive in response to false positives, which can be important for many practical problems.  Finally, I will present some very recent work on how to possibly improve Bloom filters and related data structures using machine learning techniques.