The purpose of the present paper is to improve scene results of R. Askey, P. ErdBs, G. Freud, L. Ya. Geronimus, U. Grenander, G. Szegti and P. Turan on orthogonal polynomials, Christoffel functions, orthogonal Rmr ier series, eigenvalues of Toeplitz matrices and Lagrange interpolation. In particular, Turan1 s problem will (positively) Ъе answered: is there any weight w with compact support such that for each p > 2 the Lagrange interpolating polynomials corresponding to w diverge in I? for some continuous function f? Most of the paper deals with Christoffel functions and their applications. Many limit relations for orthogonal polynomials are found in the assumption that the coefficients in the recursion formula behave nicely.