  This tutorial article showcases the many varieties and uses of quantum walks.
Discrete time quantum walks are introduced as counterparts of classical random
walks. The emphasis is on the connections and differences between the two types
of processes (with rather different underlying dynamics) for producing random
distributions. We discuss algorithmic applications for graph-searching and
compare the two approaches. Next, we look at quantization of Markov chains and
show how it can lead to speedups for sampling schemes. Finally, we turn to
continuous time quantum walks and their applications, which provide interesting
(even exponential) speedups over classical approaches.
