The paper provides an overview of the quantization and entropy coding methods in the Versatile Video Coding (VVC) standard. Special focus is laid on techniques that improve coding efficiency relative to the methods included in the High Efficiency Video Coding (HEVC) standard: The inclusion of trellis-coded quantization, the advanced context modeling for entropy coding of transform coefficient levels, the arithmetic coding engine with multi-hypothesis probability estimation, and the joint coding of chroma residuals. Beside a description of the design concepts, the paper also discusses motivations and implementation aspects. The effectiveness of the quantization and entropy coding methods specified in VVC is validated by experimental results.