Abstract: We focus in this talk on stochastic heat equations whose noisy part is of the form u W, where u is the solution to the equation and W a rather general Gaussian noise. This model is usually called parabolic Anderson model, and is related to many physically relevant systems such as KPZ equation. We will first motivate our study, then show how to define and solve the stochastic heat equation. We shall derive some Feyman-Kac representations for the solution, either in a pathwise way of for moments. These Feyman-Kac formulae always involve some weighted Brownian local times, and our goal is to include a broad class of very irregular noises into the picture. Finally, we obtain some moment estimates which entail the so-called intermittency phenomenon. If time allows it, we shall also give some perspectives on future works in this direction, concerning a sharp description of the asymptotic spatial behavior of the solution.