This paper reviews recent advances in missing data research using graphical mod- els to represent multivariate dependencies. We rst examine the limitations of tra- ditional frameworks from three di erent perspectives: transparency, estimability and testability. We then show how procedures based on graphical models can overcome these limitations and provide meaningful performance guarantees even when data are Missing Not At Random (MNAR). In particular, we identify conditions that guar- antee consistent estimation in broad categories of missing data problems, and derive procedures for implementing this estimation. Finally we derive testable implications for missing data models in both MAR (Missing At Random) and MNAR categories. Graphical Models for Processing Missing Data