The silicon photonic arrayed waveguide grating (AWG) is an important device for achieving silicon-based photonic integration. We describe the research progress in the AWG based on different device structures and various materials. The device structure mainly includes conventional symmetric AWG, reflective AWG, cascaded AWG, and AWG with a multi-mode interferometer (MMI) aperture. Compared with the conventional symmetric AWG, the reflective AWGs have smaller footprint; the cascaded AWGs have better channel crosstalk performance; the MMI-AWGs can obtain a flattened spectrum response. The silicon nanowire AWG has a very small bending radius and makes devices more compact because of the high index-contrast of silicon; the silicon nitride AWG has good channel crosstalk and polarization performance. At the end of this paper, we describe the temperature and polarization insensitive AWGs, and forecast the future development trend of silicon photonic AWGs.