Recently, the discovery of vanadium-based kagome metal AV3Sb5 (A = K, Rb, Cs) has attracted great interest in the field of superconductivity due to the coexistence of superconductivity, non-trivial surface state and multiple density waves. In this topic review, we present recent works of superconductivity and unconventional density waves in vanadium-based kagome materials AV3Sb5. We start with the unconventional charge density waves, which are thought to correlate to the timereversal symmetry-breaking orders and the unconventional anomalous Hall effects in AV3Sb5. Then we discuss the superconductivity and the topological band structure. Next, we review the competition between the superconductivity and charge density waves at different condition of pressure, chemical doping, thickness, and strains. Finally, the experimental evidences of pseudogap pair density wave are discussed.