The vanadium-based kagome metals AV3Sb5 (A = K, Rb, and Cs) host a superconducting ground state that coexists with an unconventional charge density wave (CDW). The CDW state exhibits experimental signatures of chirality, electronic nematicity, and time-reversal-symmetry-breaking, raising the questions whether the superconductivity (SC) in AV3Sb5 may also be unconventional, how SC interplays with CDW, and how the two orders evolve upon tuning. This article reviews studies of the superconducting pairing symmetry, and the tuning of SC and CDW in the AV3Sb5 compounds. Various experimental techniques consistently find that CsV3Sb5 exhibits nodeless SC, which remains robust regardless whether the CDW is present. Under hydrostatic pressure, SC in AV3Sb5 becomes enhanced as the CDW is gradually suppressed, revealing a competition between the two orders. In CsV3Sb5, a new CDW state emerges under pressure that competes more strongly with SC relative to the CDW at ambient pressure, and results in two superconducting domes that coexist with CDW. After the CDW in AV3Sb5 is fully suppressed with hydrostatic pressure, a further increase in pressure leads to a nonmonotonic evolution of the superconducting transition temperature driven by lattice modulations. Thickness is shown to be a powerful tuning parameter in AV3Sb5 thin flakes, revealing the evolution of CDW and SC upon dimensional reduction, and can be combined with hydrostatic pressure to shed light on the interplay between SC and CDW. Based on results reviewed in this article, we discuss outstanding issues to be addressed in the AV3Sb5 systems.