In this manuscript we review recent results about critical nonlinearities for some second order evolution equations, in the form \(F(s)=|s|^p\mu (|s|)\) where \(p>1\) and \(\mu \) is a modulus of continuity; the models which we take into account include wave equations and damped \(\sigma \) -evolution models; for these latter, a review about sharp lifespan estimates is also provided.