In this talk I will discuss some recent results concerning the formation of singularities for two particular kinetic equations which arise respectively in the study of quantum particles and the transport of energy in nonlinear wave systems. It turns out that the solutions of these equations can yield singularity formation in finite time. The physical significance of these singularities will be discussed. In the case of the kinetic equations for quantum particles, this singular behaviour is related to the formation of the so-called Bose-Einstein condensates, while in the case of the kinetic equations describing wave behaviour, the onset of condensates is seemingly related to the synchronization of a large class of oscillators.