Over the last few years, several new high temperature superconducting compound systems have been discovered. They have provided us with a higher transition temperature and broadened the material base for addressing some fundamental and applied issues of high temperature superconductivity. In this paper, I shall present some of our results on HgBa2Can-lCunO2n+2+6, Ba-Ca-Cu-0, and Sr-Cu-0 and discuss their implications on the roles of carrier density, the gap-symmetry, the inter-layer coupling and instabilities in high temperature superconductivity.