  This review provides a summary of the rich physics expressed within
SrTiO$_3$-based heterostructures and nanostructures. The intended audience is
researchers who are working in the field of oxides, but also those with
different backgrounds (e.g., semiconductor nanostructures). After reviewing the
relevant properties of SrTiO$_3$ itself, we will then discuss the basics of
SrTiO$_3$-based heterostructures, how they can be grown, and how devices are
typically fabricated. Next, we will cover the physics of these
heterostructures, including their phase diagram and coupling between the
various degrees of freedom. Finally, we will review the rich landscape of
quantum transport phenomena, as well as the devices that elicit them.
