Stochastic Exchange Models (SEMs) are continuous stochastic dynamics in which a certain conserved quantity is redistributed on a graph at the arrival times of a Poisson process on the edges. Examples in this class include the Averaging (AVG) process (a.k.a. repeated-averages dynamics), the Kipnis–Marchioro–Presutti (KMP) model, and their discrete counterparts. Recently, significant progress has been made in understanding the quantitative convergence of these models toward their equilibrium states, both in terms of their mixing times (e.g., the presence or absence of the cutoff phenomenon) and their spectral properties (e.g., the validity of an Aldous-like identity). In this talk, which will be based on a series of joint works with F. Sau, P. Caputo, and S. Kim, I will review some of these recent developments.