In this talk I will review the main properties of three most important classical polynomials: Hermite, Laguerre and Jacobi polynomials. I will start with Hermite,Laguerre and Jacobi equations and their solutions, and then present the main properties of these classical polynomials: Rodrigues formula, generating function,Christoffel-Darboux identities, upper bounds, recurrence relations, explicit expressions, integral representations and asymptotic expansions, by following the classical book of GaborSzego. Then I will present the famous Plemelj-Sokhotskytheorem related to additive Riemann-Hilbert problems, and the Fokas-Its-Kitaevtheorem related to the Riemann-Hilbert problems for orthogonal polynomials. As anapplication of the Fokas-Its-Kitaev theorem I will show the corresponding Riemann-Hilbert problems for Hermite, Laguerre and Jacobi polynomials. It will be also shown how we can obtain the three term recurrence relation and the differential equation for Hermite polynomials via the corresponding Riemann-Hilbert problem, by following the book of Mourad Ismail.