  We present an extensive introduction to quantum collision models (CMs), also
known as repeated interactions schemes: a class of microscopic system-bath
models for investigating open quantum systems dynamics whose use is currently
spreading in a number of research areas. Through dedicated sections and a
pedagogical approach, we discuss the CMs definition and general properties,
their use for the derivation of master equations, their connection with quantum
trajectories, their application in non-equilibrium quantum thermodynamics,
their non-Markovian generalizations, their emergence from conventional
system-bath microscopic models and link to the input-output formalism. The
state of the art of each involved research area is reviewed through dedicated
sections. The article is supported by several complementary appendices, which
review standard concepts/tools of open quantum systems used in the main text
with the goal of making the material accessible even to readers possessing only
a basic background in quantum mechanics. The paper could also be seen itself as
a friendly, physically intuitive, introduction to fundamentals of open quantum
systems theory since most main concepts of this are treated such as quantum
maps, Lindblad master equation, steady states, POVMs, quantum trajectories and
stochastic Schrodinger equation.
