Let \(A\) be a finite dimensional algebra over a field \(K\). By a module \(M\) we mean a right \(A\)-module of finite length. If \(M_ 1\) and \(M_ 2\) are indecomposable modules, we write \(M_ 1\preceq M_ 2\) if there exists a sequence \(M_ 1=X_ 1\to X_ 2\to \cdots\to X_ m=M_ 2\) of nonisomorphisms between indecomposable modules \(X_ 1,\dots,X_ m\). We denote by \(\tau M\) the Auslander-Reiten translate of \(M\). A module \(M\) (not necessarily indecomposable) is said to be directing if there do not exist indecomposable direct summands \(M_ 1\) and \(M_ 2\) of \(M\), and an indecomposable non-projective module \(W\) such that \(M_ 1\preceq\tau W\) and \(W\preceq M_ 2\). It is proved that if \(M\) is indecomposable then \(M\) is directing if and only if the relation \(M\preceq M\) does not hold. One of the main results of the paper asserts that if the quiver \(Q(A)\) of \(A\) is directed then all indecomposable \(A\)-modules are directing if and only if for all vertices \(a\) of \(Q(A)\) the radical \(\text{rad }P(a)\) of the indecomposable projective module \(P(a)\) corresponding to \(a\) is a directing module when viewed as a module over the support algebra \(A^ a\) of \(\oplus_{a\preceq b} S(b)\), where \(S(b)\) is the simple \(A\)-module corresponding to \(b\). As a consequence it is shown that if \(A\) is representation-finite, then \(A\) is representation-directed if and only if all indecomposable projective \(A\)-modules are directing.