In the first part of this talk I will discuss a recently developed abstract framework that allows us to obtain mixing rates for nonMarkov semiflows preserving an infinite measure (e.g. suspension flows over non Markov interval maps with indifferent fixed points). This is joint work with H. Bruin and I. Melbourne. In the second part, I will present a result on mixing (without rates), equivalently a local limit theorem, for non Markov flows, which requires weaker abstract assumptions. This is joint work with I. Melbourne.