  The aim of this survey is to serve as an introduction to the different
techniques available in the broad field of Aggregation-Diffusion Equations. We
aim to provide historical context, key literature, and main ideas in the field.
We start by discussing the modelling and famous particular cases: Heat
equation, Fokker-Plank, Porous medium, Keller-Segel,
Chapman-Rubinstein-Schatzman, Newtonian vortex, Caffarelli-V\'azquez,
McKean-Vlasov, Kuramoto, and one-layer neural networks. In Section 4 we present
the well-posedness frameworks given as PDEs in Sobolev spaces, and
gradient-flow in Wasserstein. Then we discuss the asymptotic behaviour in time,
for which we need to understand minimisers of a free energy. We then present
some numerical methods which have been developed. We conclude the paper
mentioning some related problems.
