The lecture is devoted to the problem of describing and calculating eigenvalues and eigenvectors of Toeplitz matrices of large order. The problems of asymptotic reversibility, Szegő type theorems on the asymptotic distribution of eigenvalues, and the properties and form of the limit of the sets of eigenvalues in the case when the order of the Toeplitz matrix tends to be infinite will be discussed. The main attention will be paid to the construction of asymptotic formulas for all eigenvalues and eigenvectors uniform over the eigenvalue number.