The theory of regularity structures enables the definition parabolic Anderson models (that is linear stochastic heat equations) in a very rough environment (namely a noise with very singular space-time covariance function). If we call u(t,x) the solution to our renormalized stochastic heat equation, in this talk we shall give some information about the moments of u(t,x) when the stochastic heat equation is interpreted in the Skorohod as well as the Stratonovich sense. Of special interest is the critical case, for which one observes a blowup of moments for large times.