Organic-inorganic hybrid solar cells display potential to be high efficiency and low cost photovoltaics due to combined advantages of high stability, high mobility and well developed fabrication process from inorganic materials and the properties to adjust organic molecule structure, absorption spectrum and bandgap from solution processable organics. Heterojunction photovoltaics formed by silicon and organics at low temperature has drawn great interests over past five years and the reported highest power conversion efficiency (PCE) has achieved up to 13.8%. The emerging of nanotechnology allows for silicon micro/nano structures including silicon nanowires, pyramids and nanocones with excellent light absorption properties which can greatly reduce the consumption of silicon materials as well as the purity dependence. The micro/nano structures also exhibit the advantages to offer larger junction area and more effective separation pathways for charge carriers. It is noticeable that silicon nanowire-based flexible hybrid solar cells with tens of micrometers silicon substrate thickness have achieved the PCE of above 12% adopting the most popular commercialized conjugated polymer poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate) (PEDOT:PSS). With the rapid developments of new organic materials and interface engineering methods, different kinds of organic-silicon hybrid solar cells has been reported and shown superior photovoltaic characteristics. The adopted organics include PEDOT:PSS, poly(3-hexylthiophene) (P3HT), 2,2',7,7'-Tetrakis-(N,N-di-4-methoxyphenylamino)-9,9'-spirobifluorene (Spiro-OMeTAD), poly(3-octylthiophene) (P3OT), fullerene derivative and so on. This paper reviews the device structures of silicon-based hybrid solar cells, working mechanism and related organic molecular. The hybrid heterojunction with different materials and fabrication processes has been discussed. The last section summarizes the method used to improve the performance of the hybrid solar cells and depicts the challenges and prospects of the silicon-based hybrid solar cells in the near future.