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.
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