  The discovery of gravitational waves, high-energy neutrinos or the
very-high-energy counterpart of gamma-ray bursts has revolutionized the
high-energy and transient astrophysics community. The development of new
instruments and analysis techniques will allow the discovery and/or follow-up
of new transient sources. We describe the prospects for the Cherenkov Telescope
Array (CTA), the next-generation ground-based gamma-ray observatory, for
multi-messenger and transient astrophysics in the decade ahead. CTA will
explore the most extreme environments via very-high-energy observations of
compact objects, stellar collapse events, mergers and cosmic-ray accelerators.
