With the unprecedented increasing demand for extremely fast processing speed and huge data capacity, traditional silicon-based information technology is becoming saturated due to the encountered bottlenecks of Moore's Law. New material systems and new device architectures are considered promising strategies for this challenge. Two-dimensional (2D) materials are layered materials and garnered persistent attention in recent years owing to their advantages in ultrathin body, strong light-matter interaction, flexible integration, and ultrabroad operation wavelength range. To this end, the integration of 2D materials into silicon-based platforms opens a new path for silicon photonic integration. In this work, a comprehensive review is given of the recent signs of progress related to 2D material integrated optoelectronic devices and their potential applications in silicon photonics. Firstly, the basic optical properties of 2D materials and heterostructures are summarized in the first part. Then, the state-of-the-art three typical 2D optoelectronic devices for silicon photonic applications are reviewed in detail. Finally, the perspective and challenges for the aim of 3D monolithic heterogeneous integration of these 2D optoelectronic devices are discussed.