A multihit capacity setup was used to study the decay of the dripline nucleus 31Ar, produced at the ISOLDE facility at CERN. A spectroscopic analysis of the β-delayed three-proton decay of 31Ar is presented for the first time together with a quantitative analysis of the β-delayed 2pγ decay. A new method for determination of the spin of low-lying levels in the βp daughter 30S using proton-proton angular correlations is presented and used to determine that the spin of the 5.2-MeV level is most likely 3+ with 4+ also possible. The half-life of 31Ar is found to be 15.1(3) ms. An improved analysis of the Fermi β strength including the β3p-decay mode gives a total measured branching ratio of 3.60(44)%, which is lower than the theoretical value found to be 4.24(43)%. Finally, a previously unidentified γ transition from the isobaric analog state in the decay of 33Ar has been found.