We reveal a previously unnoticed connection between dependency parsing and statistical machine translation (SMT), by formulating the dependency parsing task as a problem of word alignment. Furthermore, we show that two well known models for these respective tasks (DMV and the IBM models) share common modeling assumptions. This motivates us to develop an alignment-based framework for unsupervised dependency parsing. The framework (which will be made publicly available) is flexible, modular and easy to extend. Using this framework, we implement several algorithms based on the IBM alignment models, which prove surprisingly effective on the dependency parsing task, and demonstrate the potential of the alignment-based approach.