This paper reviews non-Abelian discrete groups in particle physics, focusing on their group-theoretical aspects and applications in flavor models. The authors discuss various non-Abelian discrete groups, including $ S_N $, $ A_N $, $ T' $, $ D_N $, $ Q_N $, $ \Sigma(2N^2) $, $ \Delta(3N^2) $, $ T_7 $, $ \Sigma(3N^3) $, and $ \Delta(6N^2) $, and their applications in model building. They explain how to derive conjugacy classes, characters, and representations for these groups, and discuss their breaking patterns and decompositions of multiplets. The paper also reviews anomalies of non-Abelian discrete symmetries using the path integral approach. The authors present typical flavor models using $ A_4 $, $ S_4 $, and $ \Delta(54) $ groups, and discuss the importance of non-Abelian discrete symmetries in understanding flavor physics and neutrino mixing. The paper emphasizes the role of non-Abelian discrete symmetries in controlling the flavor structure in model building and their potential as a bridge between low-energy physics and underlying theories. The authors also discuss the importance of group-theoretical aspects in determining characters and representations for these groups, and their applications in particle physics.This paper reviews non-Abelian discrete groups in particle physics, focusing on their group-theoretical aspects and applications in flavor models. The authors discuss various non-Abelian discrete groups, including $ S_N $, $ A_N $, $ T' $, $ D_N $, $ Q_N $, $ \Sigma(2N^2) $, $ \Delta(3N^2) $, $ T_7 $, $ \Sigma(3N^3) $, and $ \Delta(6N^2) $, and their applications in model building. They explain how to derive conjugacy classes, characters, and representations for these groups, and discuss their breaking patterns and decompositions of multiplets. The paper also reviews anomalies of non-Abelian discrete symmetries using the path integral approach. The authors present typical flavor models using $ A_4 $, $ S_4 $, and $ \Delta(54) $ groups, and discuss the importance of non-Abelian discrete symmetries in understanding flavor physics and neutrino mixing. The paper emphasizes the role of non-Abelian discrete symmetries in controlling the flavor structure in model building and their potential as a bridge between low-energy physics and underlying theories. The authors also discuss the importance of group-theoretical aspects in determining characters and representations for these groups, and their applications in particle physics.