  In this review we provide an introduction to the physics of a series of
frustrated quantum rare-earth pyrochlores. We first give a background on the
microscopic single- and two-ion physics of these materials, discussing the
origins and properties of their exchange interactions and their minimal
low-energy effective models, before outlining what is known about their
classical and quantum phases. We then make use of this understanding to discuss
four important material examples: Er$_2$Ti$_2$O$_7$, Yb$_2$Ti$_2$O$_7$,
Tb$_2$Ti$_2$O$_7$ and Pr$_2$Zr$_2$O$_7$, covering in some detail what is known
experimentally and theoretically for each, and summarize some key questions
that remain open. Finally, we offer an outlook on some alternative material
platforms for realizing similar physics and discuss what we see as prospects
for future investigations on these quantum rare-earth pyrochlores.
