This article provides a pedagogical review of non-Abelian discrete groups and their applications in particle physics. Non-Abelian discrete symmetries, which are finite groups, play a crucial role in model building, particularly in understanding flavor physics. The authors cover various concrete groups such as $S_N$, $A_N$, $T'$, $D_N$, $Q_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$, $T_7$, $\Sigma(3N^3)$, and $\Delta(6N^2)$. They explain group-theoretical aspects including representations, tensor products, conjugacy classes, characters, and representations for these groups. The article also discusses breaking patterns of discrete groups and decompositions of multiplets, which are important for applications. Additionally, it reviews anomalies of non-Abelian discrete symmetries and presents typical flavor models using $A_4$, $S_4$, and $\Delta(54)$ groups. The authors aim to make the content accessible to readers with a background in group theory, providing detailed explanations and examples to illustrate the concepts.This article provides a pedagogical review of non-Abelian discrete groups and their applications in particle physics. Non-Abelian discrete symmetries, which are finite groups, play a crucial role in model building, particularly in understanding flavor physics. The authors cover various concrete groups such as $S_N$, $A_N$, $T'$, $D_N$, $Q_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$, $T_7$, $\Sigma(3N^3)$, and $\Delta(6N^2)$. They explain group-theoretical aspects including representations, tensor products, conjugacy classes, characters, and representations for these groups. The article also discusses breaking patterns of discrete groups and decompositions of multiplets, which are important for applications. Additionally, it reviews anomalies of non-Abelian discrete symmetries and presents typical flavor models using $A_4$, $S_4$, and $\Delta(54)$ groups. The authors aim to make the content accessible to readers with a background in group theory, providing detailed explanations and examples to illustrate the concepts.