VERITAS, an array of atmospheric-Cherenkov telescopes sensitive to gamma rays in the very-high-energy range (VHE, E > 100 GeV), carries out an extensive multimessenger program focused on the search for electromagnetic counterparts to high-energy neutrinos and gravitational waves. As both neutrinos and gamma rays are expected to be produced in hadronic interactions near cosmic ray accelerators, the detection of a gamma-ray source in temporal and spatial coincidence with the arrival of astrophysical neutrinos could reveal cosmic ray sources and provide insights into their properties. The detection of gravitational waves by LIGO in coincidence with a gamma-ray burst has opened exciting possibilities for the study of these powerful transients. The detection of VHE gamma rays from these sources would not only help in pinpointing an electromagnetic counterpart to the gravitational-wave event, but also enable the study of the relativistic shocks responsible for the high-energy emission. This talk will present an overview of the VERITAS multimessenger program, highlighting recent results from the search of VHE gamma-ray sources associated with neutrino and gravitational-wave events and discuss future plans for these studies.