  Coherent quantum optics, where the interaction of a photon with an emitter
does not scramble phase coherence, lies at the heart of many quantum optical
effects and emerging technologies. Solid-state emitters coupled to nanophotonic
waveguides are a promising platform for quantum devices, as this combination is
scalable. Yet, reaching full coherence in these systems is challenging due to
the dynamics of the solid-state environment of the emitters. Here, we review
progress towards coherent light-matter interactions with solid-state quantum
emitters coupled to nanophotonic waveguides. We first lay down the theoretical
foundation for coherent and nonlinear light-matter interactions of a two-level
system in a quasi-one-dimensional system, and then benchmark experimental
realizations. We then discuss higher-order nonlinearities that arise due to the
addition of photons of different frequencies, more complex energy-level schemes
of the emitters, and the coupling of multiple emitters via a shared photonic
mode. Throughout, we highlight protocols for applications and novel effects
that are based on these coherent interactions, the steps taken towards their
realization, and the challenges that remain to be overcome.
