This survey presents an overview of the theory of orthogonal polynomials of one variable, excluding those on the unit circle. The theory is divided into two main parts: the algebraic aspect, which is closely related to special functions, combinatorics, and algebra, and the analytical aspect, which is more focused on analysis and its connections to other areas of mathematics. The algebraic part deals with concrete orthogonal systems, such as Jacobi, Hahn, and Askey-Wilson polynomials, while the analytical part focuses on questions typical of analysis, such as orthogonal polynomials on the real line and the unit circle. Orthogonal polynomials are defined with respect to a measure or an inner product, and they have a wide range of applications in mathematics, including continued fractions, Padé approximation, the moment problem, spectral theory of self-adjoint operators, quadrature, and random matrices. The theory of orthogonal polynomials is also closely related to the study of the Riemann-Hilbert problem, which provides a powerful method for analyzing the asymptotic behavior of orthogonal polynomials. The survey discusses various aspects of orthogonal polynomials, including their recurrence relations, zeros, and asymptotic behavior. It also covers classical orthogonal polynomials such as Jacobi, Laguerre, and Hermite polynomials, as well as more general cases such as matrix orthogonal polynomials, non-Hermitian orthogonal polynomials, and multiple orthogonal polynomials. The survey also touches on the connection between orthogonal polynomials and other areas of mathematics, such as harmonic analysis on spheres and balls, approximation theory, and random matrices. The survey concludes with a discussion of the role of orthogonal polynomials in various areas of mathematics, including approximation theory, interpolation, and the study of the spectral properties of self-adjoint operators. It also highlights the importance of orthogonal polynomials in the study of random matrices and their connection to the distribution of eigenvalues. The survey emphasizes the importance of orthogonal polynomials in both theoretical and applied mathematics, and it provides a comprehensive overview of the current state of the theory.This survey presents an overview of the theory of orthogonal polynomials of one variable, excluding those on the unit circle. The theory is divided into two main parts: the algebraic aspect, which is closely related to special functions, combinatorics, and algebra, and the analytical aspect, which is more focused on analysis and its connections to other areas of mathematics. The algebraic part deals with concrete orthogonal systems, such as Jacobi, Hahn, and Askey-Wilson polynomials, while the analytical part focuses on questions typical of analysis, such as orthogonal polynomials on the real line and the unit circle. Orthogonal polynomials are defined with respect to a measure or an inner product, and they have a wide range of applications in mathematics, including continued fractions, Padé approximation, the moment problem, spectral theory of self-adjoint operators, quadrature, and random matrices. The theory of orthogonal polynomials is also closely related to the study of the Riemann-Hilbert problem, which provides a powerful method for analyzing the asymptotic behavior of orthogonal polynomials. The survey discusses various aspects of orthogonal polynomials, including their recurrence relations, zeros, and asymptotic behavior. It also covers classical orthogonal polynomials such as Jacobi, Laguerre, and Hermite polynomials, as well as more general cases such as matrix orthogonal polynomials, non-Hermitian orthogonal polynomials, and multiple orthogonal polynomials. The survey also touches on the connection between orthogonal polynomials and other areas of mathematics, such as harmonic analysis on spheres and balls, approximation theory, and random matrices. The survey concludes with a discussion of the role of orthogonal polynomials in various areas of mathematics, including approximation theory, interpolation, and the study of the spectral properties of self-adjoint operators. It also highlights the importance of orthogonal polynomials in the study of random matrices and their connection to the distribution of eigenvalues. The survey emphasizes the importance of orthogonal polynomials in both theoretical and applied mathematics, and it provides a comprehensive overview of the current state of the theory.