Asymmetric Numeral Systems (ANS) proposed by Jarek Duda are high-performance distortionless data compression schemes that can achieve almost the same compression performance as arithmetic codes with less arithmetic operations than arithmetic coding. The ANS is widely used in various practical systems like Facebook, Apple, Google, Dropbox, Microsoft, and Pixar, due to their high performance, but many researchers still lack much knowledge about the ANS. This paper thoroughly explains the encoding and decoding algorithms of the ANS, and theoretically analyzes the average code length achievable by the ANS.