Abstract: The spreading model of a weakly null sequence in a Banach space X is a certain Banach space Y with an unconditional basis which is finitely representable in X. Since Banach spaces with unconditional bases must either be reflexive or contain isomorphic copies of c_0 or l_1, it was asked by V.D. Milman whether every Banach space X admits a spreading model which is reflexive or it is isomorphic to c_0 or l_1. Also, it was asked by H. Rosenthal whether a separable infinite dimensional Banach space X must admit a spreading model that is isomorphic to c_0 (or l_1) in the case that X admits spreading models "arbitrarily close to" c_0 (or l_1). I will present a joint work with E. Odell and Th. Schlumprecht where we give negative answers to all three above questions.