Let X be a unruled fourfold. According to the diagonal decomposition of Bloch-Srinivas, it is known that the Hodge conjecture holds on degree 4 Hodge classes of X with rational coefficients. An interesting question is to know wether the Hodge conjecture holds for integral Hodge classes on X. In this lecture, we will talk about this problem for some families of rationally connected threefolds.