  These are the notes for a course at the 18th Brazilian School of Probability
held from August 3rd to 9th, 2014 in Mambucaba. The aim of the course is to
introduce the basic problems of non--linear PDEs with stochastic and irregular
terms. We explain how it is possible to handle them using two main techniques:
the notion of energy solutions and that of paracontrolled distributions. In
order to maintain a link with physical intuitions, we motivate such singular
SPDEs via a homogenisation result for a diffusion in a random potential.
