In order to study the Kähler and Mori cones of a hyperkähler manifold \(X\), the article introduces the notion of wall divisors on \(X\). It is shown that the class of wall divisors is preserved under smooth deformations of \(X\). Furthermore, a one-to-one correspondence is established between certain wall-divisors and negative extremal rays of the Mori cone of \(X\). This correspondence can be exploited to obtain numerical characterizations of the Kähler and Mori cones of \(X\). As an application, the article considers the case where \(X\) is of \(K3^{[n]}\) type. A full numerical description of the Kähler and Mori cones is given in this case for \(n = 2\), \(3\) and \(4\).