Automatic word alignment plays a critical role in statistical machine translation. Unfortunately, the relationship between alignment quality and statistical machine translation performance has not been well understood. In the recent literature, the alignment task has frequently been decoupled from the translation task and assumptions have been made about measuring alignment quality for machine translation which, it turns out, are not justified. In particular, none of the tens of papers published over the last five years has shown that significant decreases in alignment error rate (AER) result in significant increases in translation performance. This paper explains this state of affairs and presents steps towards measuring alignment quality in a way which is predictive of statistical machine translation performance.