Integrated quantum photonics is now seen as one of the promising approaches to realize scalable quantum information systems. With optical waveguides based on silicon photonics technologies, we can realize quantum optical circuits with a higher degree of integration than with silica waveguides. In addition, thanks to the large nonlinearity observed in silicon nanophotonic waveguides, we can implement active components such as entangled photon sources on a chip. In this paper, we report recent progress in integrated quantum photonic circuits based on silicon photonics. We review our work on correlated and entangled photon-pair sources on silicon chips, using nanoscale silicon waveguides and silicon photonic crystal waveguides. We also describe an on-chip quantum buffer realized using the slow-light effect in a silicon photonic crystal waveguide. As an approach to combine the merits of different waveguide platforms, a hybrid quantum circuit that integrates a silicon-based photon-pair source and a silica-based arrayed waveguide grating is also presented.