Topology optimization has become an important part of the structural design process; by finding the optimal layout of a material in a domain, subject to some constraint, an informed initial design can be found early on and potentially save both time and costs in the iterative design procedure. The field has continuously evolved by developing different numerical methods and approaches, as well as in its application to an increasingly wider range of physical disciplines. The aim of this document is to give an introduction to the field of topology optimization by giving a basic overview of the main methods and approaches used as well as providing an up-to-date review of recent literature concerning physical disciplines with applications of topology optimization that can be relevant to aircraft design, namely elastic structures possibly involving multi-scale or anisotropic material properties, fluid-structure interaction, and radar cross section properties. In addition we present a list of available opensource software that either implement a general approach using some of the well-used methods in topology optimization or a more specific approach connected to a particular study.