The theory of mean-field interacting particle models had certainly started by the mid-1960s, with the work of Henry P. McKean Jr. on Markov interpretations of a class of nonlinear parabolic partial differential equations arising in fluid mechanics. The mathematical foundations of these classes of models were developed from the mid-1980s to the mid-1990s by several mathematicians, including Werner Braun, Klaus Hepp, Karl Oelschläger, Gérard Ben Arous and Marc Brunaud, Donald Dawson, Jean Vaillancourt and Jürgen Gärtner, Christian Léonard, Sylvie Méléard, Sylvie Roelly, Alain-Sol Sznitman and Hiroshi Tanaka for diffusion type models; F. Alberto Grünbaum, Tokuzo Shiga, Hiroshi Tanaka, Sylvie Méléard and Carl Graham for general classes of interacting jump-diffusion processes.