Composed of a large number of artificial nanostructures, metasurfaces have found applications in metalenses, structured light generation and optical deflectors through wavefront shaping. After careful design according to optical requirements, metasurfaces can achieve independent functions under different incident light conditions. Deep learning emerges as a transformative design approach in nanophotonics, providing nanostructures tailored to various optical requirements. A statistic relationship between geometric shapes and optical properties is hidden in massive nanostructures. The relationship is learned without any help of physical models, opening a possibility for further research on multifunctional metasurface. Here, different optical dimensions multiplexed in metasurfaces are reviewed, and combining these multiplexing methods into one metasurface can significantly increase functional channels. Then different types of neural networks applied in metasurface design are introduced, opening a possibility to combine the various optical multiplexing. Furthermore, the constructive suggestions are provided on multifunctional metasurface designed by deep learning, and specific opinions on future developments are discussed.