Polynomial Szemeredi Theorem (joint result with A Leibman) states that if pi, i = 1, 2, . . . , k are polynomials with integer coefficients which satisfy pi(0) = 0, then any set A in N which has positive upper density contains “many” polynomial configurations of the form a, a + p1(n), a + p2(n), . . . , a + pk(n). (The classical Szemeredi theorem corresponds to the case where pi(n) = in, i = 1, 2, . . . , k). We will discuss a new extension of the Polynomial Szemeredi Theorem which deals with the “upgrade” of the Polynomial Szemeredi Theorem to the so called generalized polynomials, namely functions which are obtained from regular polynomials via iterated use of the floor function (joint work with Randall McCutcheon).