  The quantum collision models are a useful method to describe the dynamics of
an open quantum system by means of repeated interactions between the system and
some particles of the environment, which are usually termed "ancillas". In this
paper, we review the main collision models for the dynamics of multipartite
open quantum systems, which are composed of several subsystems. In particular,
we are interested in models that are based on elementary collisions between the
subsystems and the ancillas, and that simulate global and/or local Markovian
master equations in the limit of infinitesimal timestep. After discussing the
mathematical details of the derivation of a generic collision-based master
equation, we provide the general ideas at the basis of the collision models for
multipartite systems, we discuss their strengths and limitations, and we show
how they may be simulated on a quantum computer. Moreover, we analyze some
properties of a collision model based on entangled ancillas, derive the master
equation it generates for small timesteps, and prove that the coefficients of
this master equation are subject to a constraint that limits their generality.
Finally, we present an example of this collision model with two bosonic
ancillas entangled in a two-mode squeezed thermal state.
