Summary: An antimagic labeling of an undirected graph \(G\) with \(n\) vertices and \(m\) edges is a bijection from the set of edges of \(G\) to the integers \(\{1, \dots , m\}\) such that all \(n\) vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with that vertex. A graph is called antimagic if it admits an antimagic labeling. In N. Hartsfield and G. Ringel, Pearls in Graph Theory (1990; Zbl 0703.05001), pp. 108–109), Hartsfield and Ringel conjectured that every simple connected graph, other than \(K_{2}\), is antimagic. Despite considerable effort in recent years, this conjecture is still open. In this article we study a natural variation; namely, we consider antimagic labelings of directed graphs. In particular, we prove that every directed graph whose underlying undirected graph is “dense” is antimagic, and that almost every undirected \(d\)-regular graph admits an orientation which is antimagic.