Volkas has made seminal contributions to theoretical particle physics, early-universe cosmology and high-energy astrophysics. His most important work includes the discovery of the neutrino-oscillation-induced neutrino asymmetry generation mechanism (important for primordial nucleosynthesis), the exploration of atmospheric neutrino phenomenology, the invention of the mirror-matter model and its application to neutrino physics and the dark matter problem, pioneering studies on neutrino emission from the Galactic centre, an explanation of electric-charge quantization using standard physics only, studies in the persistence of quantal coherence despite strong system-environment coupling, and a novel symmetry-breaking mechanism for brane-world models.