The document summarizes the key stages of the Elixir compilation process: 1. Elixir code is parsed and tokenized into an Elixir Abstract Syntax Tree (AST). 2. All Elixir macros are expanded in the AST. 3. The expanded AST is translated into an Erlang AST, which is then fed into the Erlang compiler to produce BEAM bytecode that can be executed by the BEAM virtual machine.