  Astroparticle physics is undergoing a profound transformation, due to a
series of extraordinary new results, such as the discovery of high-energy
cosmic neutrinos with IceCube, the direct detection of gravitational waves with
LIGO and Virgo, and many others. This white paper is the result of a
collaborative effort that involved hundreds of theoretical astroparticle
physicists and cosmologists, under the coordination of the European Consortium
for Astroparticle Theory (EuCAPT). Addressed to the whole astroparticle physics
community, it explores upcoming theoretical opportunities and challenges for
our field of research, with particular emphasis on the possible synergies among
different subfields, and the prospects for solving the most fundamental open
questions with multi-messenger observations.
