Untyped dependency parsing can be viewed as the problem of finding maximum spanning trees (MSTs) in directed graphs. Using this representation, the Eisner (1996) parsing algorithm is sufficient for searching the space of projective trees. More importantly, the representation is extended naturally to non-projective parsing using Chu-Liu-Edmonds (Chu and Liu, 1965; Edmonds, 1967) MST algorithm. These efficient parse search methods support large-margin discriminative training methods for learning dependency parsers. We evaluate these methods experimentally on the English and Czech treebanks.