  This survey article is devoted to general results in combinatorial
enumeration. The first part surveys results on growth of hereditary properties
of combinatorial structures.
  These include permutations, ordered and unordered graphs and hypergraphs,
relational structures, and others. The second part advertises five topics in
general enumeration: 1. counting lattice points in lattice polytopes, 2. growth
of context-free languages, 3. holonomicity (i.e., P-recursiveness) of numbers
of labeled regular graphs, 4. frequent occurrence of the asymptotics
cn^{-3/2}r^n and 5. ultimate modular periodicity of numbers of MSOL-definable
structures.
