Multimode silicon photonics is attracting more and more attention because the introduction of higher-order modes makes it possible to increase the channel number for data transmission in mode-division-multiplexed (MDM) systems as well as improve the flexibility of device designs. On the other hand, the design of multimode silicon photonic devices becomes very different compared with the traditional case with the fundamental mode only. Since not only the fundamental mode but also the higher-order modes are involved, one of the most important things for multimode silicon photonics is the realization of effective mode manipulation, which is not difficult, fortunately because the mode dispersion in multimode silicon optical waveguide is very strong. Great progresses have been achieved on multimode silicon photonics in the past years. In this paper, a review of the recent progresses of the representative multimode silicon photonic devices and circuits is given. The first part reviews multimode silicon photonics for MDM systems, including on-chip multichannel mode (de)multiplexers, multimode waveguide bends, multimode waveguide crossings, reconfigurable multimode silicon photonic integrated circuits, multimode chip-fiber couplers, etc. In the second part, we give a discussion about the higher-order mode-assisted silicon photonic devices, including on-chip polarization-handling devices with higher-order modes, add-drop optical filters based on multimode Bragg gratings, and some emerging applications.