We summarize the structural features of several Cu-based alloys known so far having high glass-forming ability and investigate the influence of Ag addition on their crystallization behavior. According to synchrotron-beam X-ray radiation studies, an oC68 Cu10Zr7 phase is found to be a good approximant to the Cu-Zr-Ti and Cu-Zr-Ag glassy phases. The structure of the bulk glassy Cu36Zr48Al8Ag8 and Cu44Ag15Zr36Ti5 alloy samples studied by high-resolution TEM was found to contain well developed medium-range order zones and nanoparticles, respectively. An influence of the cooling rate on the structure and properties of the Cu-based glassy alloys on heating was also studied. The crystallization kinetics of Cu55Zr45, Cu 50Zr50, Cu55-xZr45Agx (x 0, 10, 20), Cu44Ag15Zr36Ti5, Cu 45Zr45Al5Ag5 and Cu 36Zr48Al8Ag8 glassy alloys was also analyzed substantially. Cu35Zr45Ag20 alloy was found to exhibit possible phase separation upon heating within a supercooled liquid region.