The field of transition-metal kagome materials has leapt forward with the discovery of vanadium-based, nonmagnetic kagome superconductors AV₃Sb₅ (A=K, Cs, Rb). Central to the revelation is a cascade of correlated quantum states triggered by an unconventional 3Q charge density wave (CDW) order. We review recent experimental findings, focusing on evidence for time-reversal symmetry breaking in both the normal and the superconducting state. We argue that the essential phenomenology can be captured by a loop-current CDW order, realizable in models with extended Coulomb interactions on the kagome lattice. The loop-current Chern metal has a partially filled Chern band and Chern Fermi pockets carrying concentrated Berry curvature. We discuss how Cooper pairing over the Chern Fermi pockets produces a chiral topological superconductor with three pairing components whose relative phases are locked at 120-degrees, giving rise to a vortex-antivortex lattice of a novel roton pair density wave (PDW). Such a chiral state is frustrated on the kagome lattice and strong relative phase fluctuations suppress the true transition temperature, resulting in an extended region of superconducting fluctuations. We argue that charge-6e and charge-4e paired states, free of the chiral phase frustration, emerge over the extended fluctuation region upon melting of the charge-2e chiral superconductor, leading to fractionalized flux quantization and higher-charge superconductivity. The connections to the most recent experimental observations will be discussed.