The rate-distortion optimized quantization (RDOQ) provides an excellent trade-off between rate and distortion in High Efficiency Video Coding (HEVC), leading to inspiring improvement in terms of rate-distortion performance. However, its heavy use imposes high complexity on the encoder in realworld video compression applications. In this paper, we provide a comprehensive review on low complexity quantization techniques in HEVC, including both fast RDOQ and all-zero block detection. In particular, the fast RDOQ relies on rate and distortion models for rate-distortion cost estimation, such that the most appropriate quantized coefficient is selected in a low complexity way. All-zero block detection infers the all-zero block by skipping transform and quantization, in an effort to further reduce the complexity. The relationship between the two techniques is also discussed, and moreover, we also envision the future design of low complexity quantization in the upcoming Versatile Video Coding (VVC) standard. INDEX TERMS High efficiency video coding, low complexity video coding, rate-distortion optimized quantization.