THESEUS is a space mission concept, currently under Phase A study by ESA as candidate M5 mission, aiming at exploiting Gamma-Ray Bursts for investigating the early Universe and at providing a substantial advancement of multi-messenger and time-domain astrophysics. In addition to fully exploiting high-redshift GRBs for cosmology (pop-III stars, cosmic re-ionization, SFR and metallicity evolution up to the cosmic dawn), THESEUS will allow the identification and study of the electromagnetic counterparts to sources of gravitational waves which will be routinely detected in the late 20s / early 30s by next generation facilities like aLIGO/aVirgo, LISA, KAGRA, and Einstein Telescope (ET), as well as of most classes of X/gamma-ray transient sources, thus providing an ideal synergy with the large e.m. facilities of the near future like, e.g., LSST, ELT, TMT, SKA, CTA, ATHENA. These breakthrough scientific objectives will be achieved by an unprecedented combination of X/gamma-ray monitors, providing the capabilities of detecting and accurately localize and kind of GRBs and may classes of transient in an energy band as large as 0.1 keV - 10 MeV, with an on-board NIR telescope providing detection, localization (arcsec) and redshift measurement of the NIR counterpart. A Guest Observer programme, further improving the scientific return and community involvement is also envisaged. We summarize the main scientific requirements of the mission and provide an overview of the updated concept, design (instruments and spacecraft) and mission profile.