The research history of accretion disks and flow is overviewed with special attention to the impacts of the disk-instability model. The standard disk model was built under (radially) one-dimensional approximation and had some success in describing the basic properties of the accreting systems. However, this model is known to break down under several circumstances. Alternative models have been proposed as an extension of the standard disk model. The disk-instability model is one of such attempts and is unique in providing us with rich information regarding the time-dependent properties of accretion disks. We first show the necessity of solving the multi-zone vertical structure to incorporate convective energy transport, which is required for producing S-shaped equilibrium curves. We next introduce two-zone models for disk-corona structure and discuss how to reproduce observational properties. We finally discuss the time-dependent properties of accretion disks undergoing dwarf-nova type disk instability and its applications to the X-ray binaries.