Some recent progress in singular stochastic partial differential equations

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent progress in defining, approximating, and studying the properties of a few examples of such equations. We focus mainly on the dynamical Φ 4 Φ ^4 equation, the KPZ equation, and the parabolic Anderson model, as well as a few other equations which arise mainly in physics.