  This document is an announcement and preview of a memoir whose full version
is available on the Open Math Notes repository of the American Mathematical
Society (OMN:202109.111309). In this memoir, I try to provide a fairly
comprehensive picture of (mostly shallow water) asymptotic models for water
waves. The work and presentation is heavily inspired by the book of D. Lannes,
yet extends the discussion into several directions, notably high order and
fully dispersive models, and internal/interfacial waves.
