  Despite their long history and astrophysical importance, some of the key
properties of neutron stars are still uncertain. The extreme conditions
encountered in their interiors, involving matter of uncertain composition at
extreme density and isospin asymmetry, uniquely determine the stars'
macroscopic properties within General Relativity. Astrophysical constraints on
those macroscopic properties, such as neutron star masses and radii, have long
been used to understand the microscopic properties of the matter that forms
them. In this article we discuss another astrophysically observable macroscopic
property of neutron stars that can be used to study their interiors: their
tidal deformation. Neutron stars, much like any other extended object with
structure, are tidally deformed when under the influence of an external tidal
field. In the context of coalescences of neutron stars observed through their
gravitational wave emission, this deformation, quantified through a parameter
termed the \emph{tidal deformability}, can be measured. We discuss the role of
the tidal deformability in observations of coalescing neutron stars with
gravitational waves and how it can be used to probe the internal structure of
Nature's most compact matter objects. Perhaps inevitably, a large portion of
the discussion will be dictated by GW170817, the most informative confirmed
detection of a binary neutron star coalescence with gravitational waves as of
the time of writing.
