Collective excitation modes are a characteristic feature of symmetry-broken phases of matter. Their properties are of fundamental interest due to the distinguishing feature of any symmetry-broken phase such as superconductors, charge density waves or antiferromagnets. An amplitude Higgs mode and a phase modes of a superconductor are the radial and angular excitations in the Mexican-hat potential of the free energy. There exist an additional Leggett phase mode for a two-band superconductor. However, these Higgs and Leggett modes have never been simultaneously detected in any known two-band superconductors. There has been no clue for their evolution or development with tunable physical parameters such as temperature, doping, pressure, or magnetic fields. The great achievement in the study of high-temperature superconductivity in cuprates was the experimental findings of charge density waves and their competition with superconductivity in certain doping regime in the past 5 years. Since there is a close relation between the charge density wave and pseudogap in these superconductors, the complicated phase diagram is then simplified to the one solely including charge density wave and superconductivity. In this talk, I will first show our recent results of the emergence of the charge density wave in the overdoped region even at room temperature in a trilayer cuprate Tl2223 and the reduction of the superconducting transition temperature. Then a superconductor NbSe2, sharing the common simplified phase diagram with cuprates, is chosen to show how we detect Higgs and Leggett modes in this two-band superconductor by using Raman scattering technique and how these modes evolve with pressure upon heavy compression. The implications of such observations to the understanding of superconductivity in two-dimensional superconductors, cuprates, and our newly discovered molecule superconductors will be discussed.