We have studied the vortex state problem systematically in YBa2Cu3O7-y system with twinned/untwinned single crystals. Different vortex states are observed on samples with different characteristics. Our detailed I - V characteristics measured in different magnetic fields, at temperature below where the resistive ”knee” occurs, show that the dynamics of the vortex motion depends on the sample characteristics and field strength. Under an intermediate external field, vortex lattice phenomenon is observed in untwinned and some twinned single crystals. On the other hand, vortex glass (or solid) state is observed in twinned crystals with strong pinning effect. In high external magnetic field region, the low resistivity data fit nicely to giant flux-creep model, predicted by Tinkham.