The Cherenkov Telescope Array (CTA) will be the next generation ground-based very-high-energy (VHE) gamma-ray observatory. The first of the Large Size Telescopes (LST1), is already under commissioning at Roque de los Muchachos observatory, in La Palma. The unprecedented sensitivity at short timescales of CTA will make of this observatory the leading instrument for the discovery of new transient events of both Galactic and extragalactic origin in the VHE regime. It will unveil the physics of the most extreme objects in the Universe and their interaction with the surrounding environment. The recent discoveries of the first gamma-ray bursts (GRBs) at VHE, the connection between gravitational waves and short GRBs and the association of an extragalactic neutrino with a flaring blazar, have opened new lines of research in multi-messenger and transient astrophysics. The detections of these different cosmic messengers have shown the importance of coordinated campaigns. CTA will perform follow-up observations of these events and open a new window for time-domain astrophysics at VHE. The Transient program is one of the Key Science Projects of CTA. This program includes a wide range of sources in a multi-messenger and multi-wavelength context, ranging from GRBs, to gravitational waves, energetic neutrinos, core-collapse supernovae and Galactic transients (such as microquasars, pulsar wind nebulae or novae). In this contribution, I will present the results of the exploration of the capabilities of CTA to detect new transient astrophysical phenomena at VHE.