The scientific potential of the Cherenkov Telescope Array (CTA) is extremely broad: from understanding the role of relativistic cosmic particles, to the search for dark matter. CTA will be an explorer of the extreme universe, surveying the high-energy sky hundreds of times faster than previous TeV telescopes. The angular resolution of CTA will approach 1 arc-minute at high-energies -- the best resolution of any instrument above the X-ray band. With over an order-of-magnitude collection area improvement, CTA will be, for example, three orders of magnitude more sensitive on hour timescales than the Fermi-LAT at the 30 GeV range. Furthermore, the observatory will operate arrays on sites in both hemispheres to provide full sky coverage and hence maximize its discovery potential of rare phenomena such as nearby supernovae, GRBs or gravitational wave transients. The first CTA telescope has been inaugurated in the Canary Islands in 2018, and as more telescopes are added in the coming years, flexible operation will be possible, with sub-arrays available for performing specific tasks. All this considered, CTA will have important synergies with many of the new generation, major astronomical and astroparticle observatories. Multi-wavelength and multi-messenger approaches combining CTA data with those from other instruments will lead to a deeper understanding of the broad-band non-thermal properties of target sources, elucidating the nature and environment of gamma-ray emitters. In this talk I will introduce the broad scope of CTA science, and present some specific science cases and multi-instrumental synergies, as well as the potential for cooperation of other wavebands and astronomical messengers with CTA.