<p>Spontaneous collapse models (SCM) employ an imaginary noise term in the modification of Schrödinger’s equation in order to achieve a stochastic collapse process. Such noise term is typically assumed to be white, and therefore uncorrelated in time, which results in the dynamics being Markovian. In the first part of this paper I discuss the reasons why physicists are exploring the possibility to instead employ non-white stochastic noise terms in the dynamics of SCM, and I then briefly introduce these models. In the second part, my aim is to provide an evaluation of the major conceptual and philosophical consequences of the generalised collapse models with colored noise. In particular, I will focus on the broad class of implications having to do with the non-Markovian nature of the dynamics, with its resulting temporal non-locality, and on the possibility to consider the noise field as a real physical entity.</p>