  Drift theory is an intuitive tool for reasoning about random processes: It
allows turning expected stepwise changes into expected first-hitting times.
While drift theory is used extensively by the community studying randomized
search heuristics, it has seen hardly any applications outside of this field,
in spite of many research questions that can be formulated as first-hitting
times.
  We state the most useful drift theorems and demonstrate their use for various
randomized processes, including the coupon collector process, winning streaks,
approximating vertex cover, and a random sorting algorithm. We also consider
processes without expected stepwise change and give theorems based on drift
theory applicable in such scenarios. We use these theorems for the analysis of
the gambler's ruin process, for a coloring algorithm, for an algorithm for
2-SAT, and for a version of the Moran process without bias. A final tool we
present is a tight theorem for processes on finite state spaces, which we apply
to the Moran process.
  We aim to enable the reader to apply drift theory in their own research to
derive accessible proofs and to teach it as a simple tool for the analysis of
random processes.
