A guide to the Choquard equation

We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$\begin{aligned} -\Delta u + V(x)u = \left( |x|^{-(N-\alpha )} *|u |^p\right) |u |^{p - 2} u \quad \text {in} \ \mathbb {R}^N, \end{aligned}$$-Δu+V(x)u=|x|-(N-α)∗|u|p|u|p-2uinRN,and some of its variants and extensions.