High-speed optical interconnects of data centers and high performance computers (HPC) have become the rapid development direction in the field of optical communication owing to the explosive growth of market demand. Currently, optical interconnect systems are moving towards higher capacity and integration. High-sensitivity receivers with avalanche photodiodes (APDs) are paid more attention due to the capability to enhance gain bandwidth. The impact ionization coefficient ratio is one crucial parameter for avalanche photodiode optimization, which significantly affects the excess noise and the gain bandwidth product (GBP). The development of silicon-germanium (Si-Ge) APDs are promising thanks to the low impact ionization coefficient ratio of silicon, the simple structure, and the CMOS compatible process. Separate absorption charge multiplication (SACM) structures are typically adopted in Si-Ge APDs to achieve high bandwidth and low noise. This paper reviews design and optimization in high-speed Si-Ge APDs, including advanced APD structures, APD modeling and APD receivers.