Human beings are entering a Big Data era, which has significantly boosted the current digital economy and society. But in reality, all current data storage technologies and mediums can only store less than half of what we generate, which means most of the data will be forcibly lost if without breakthrough in high-capacity storage technologies. However, Ernst Abbe set a fundamental barrier that limits the smallest feature size of a recording voxel to approximately half of the wavelength. Alternatively, this limitation could be overcome by implementing multiplex technology. In this review, techniques employed various multiplex dimensions such as 3D space, polarization and wavelength are briefly introduced. Especially, we highlight the development history, current state of the art and urgent challenges of five-dimensional optical data storage based on laser-induced nanogratings.