  The field of classical stochastic processes forms a major branch of
mathematics. They are, of course, also very well studied in biology, chemistry,
ecology, geology, finance, physics, and many more fields of natural and social
sciences. When it comes to quantum stochastic processes, however, the topic is
plagued with pathological issues that have led to fierce debates amongst
researchers. Recent developments have begun to untangle these issues and paved
the way for generalizing the theory of classical stochastic processes to the
quantum domain without ambiguities. This tutorial details the structure of
quantum stochastic processes, in terms of the modern language of quantum combs,
and is aimed at students in quantum physics and quantum information theory. We
begin with the basics of classical stochastic processes and generalize the same
ideas to the quantum domain. Along the way, we discuss the subtle structure of
quantum physics that has led to troubles in forming an overarching theory for
quantum stochastic processes. We close the tutorial by laying out many exciting
problems that lie ahead in this branch of science.
