  This review provides an overview of recent advances in multi-wavelength and
multi-messenger observations of blazars, the current status of theoretical
models for blazar emission, and prospects for future facilities. The discussion
of observational results will focus on advances made possible through the Fermi
Gamma-Ray Space Telescope and ground-based gamma-ray observatories (H.E.S.S.,
MAGIC, VERITAS) as well as the recent first evidence for a blazar being a
source of IceCube neutrinos. The main focus of this review will be the
discussion of our current theoretical understanding of blazar multi-wavelength
and multi-messenger emission, in the spectral, time, and polarization domains.
Future progress will be expected in particular through the development of the
first X-ray polarimeter, IXPE, and the installation of the Cherenkov Telescope
Array (CTA), both expected to become operational in the early to mid 2020s.
