HPSG assumes Phrase Structure (PS), a partonomy, in contrast with Dependency Grammar (DG), which recognises Dependency Structure (DS), with direct relations between individual words and no multi-word phrases. The chapter presents a brief history of the two approaches, showing that DG matured in the late nineteenth century, long before the influential work by Tesni��re, while Phrase Structure Grammar (PSG) started somewhat later with Bloomfield's enthusiastic adoption of Wundt's ideas. Since DG embraces almost as wide a range of approaches as PSG, the rest of the chapter focuses on one version of DG, Word Grammar. The chapter argues that classical DG needs to be enriched in ways that bring it closer to PSG: each dependent actually adds an extra node to the head, but the nodes thus created form a taxonomy, not a partonomy; coordination requires strings; and in some languages the syntactic analysis needs to indicate phrase boundaries. Another proposed extension to bare DG is a separate system of relations for controlling word order, which is reminiscent of the PSG distinction between dominance and precedence. The ``head-driven'' part of HPSG corresponds in Word Grammar to a taxonomy of dependencies which distinguishes grammatical functions, with complex combinations similar to HPSG's re-entrancy. The chapter reviews and rejects the evidence for headless phrases, and ends with the suggestion that HPSG could easily move from PS to DG.