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Explicit and implicit experimental evidence for charge density wave (CDW) presence in high-Tc superconducting oxides is analyzed. The theory of CDW superconductors is presented. It is shownthat the observed pseudogaps and dip-hump structures in tunnel and photoemission spectra aremanifestations of the same CDW gapping of the quasiparticle density of states. Huge pseudogapsare transformed into modest dip-hump structures at low temperatures, T, when the electron spectrum superconducting gapping dominates. Heat capacity jumps at the superconducting critical temperature and the paramagnetic limit are calculated for CDW superconductors. For a certainrange of parameters, the CDW state in a d-wave superconductor becomes reentrant with T, the main control quantity being a portion of dielectrcally gapped Fermi surface. It is shown that inthe weak-coupling approximation, the ratio between the superconducting gap at zero temperatureΔ(T=0) and Tc has the Bardeen-Cooper-Schrieffer value for s-wave Cooper pairing and exceedsthe corresponding value for d-wave pairing of CDW superconductors. Thus, large experimentallyfound values 2Δ(T=0)/Tc≈5÷8 are easily reproduced with reasonable input parameter values ofthe model. The conclusion is made that CDWs play a significant role in cuprate superconductivity

Competition of Superconductivity and Charge Density Waves in Cuprates: Recent Evidence and Interpretation