Numerical quadratures and orthogonal polynomials

Orthogonal polynomials of different kinds as the basic tools play very important role in construction and analysis of quadrature formulas of maximal and nearly maximal algebraic degree of exactness. In this survey paper we give an account on some important connections between orthogonal polynomials and Gaussian quadratures, as well as several types of generalized orthogonal polynomials and corresponding types of quadratures with simple and multiple nodes. Also, we give some new results on a direct connection of generalized Birkhoff-Young quadratures for analytic functions in the complex plane with multiple orthogonal polynomials.