This paper gives an overview of the latest developments in computational syntactic analysis of Estonian. We present Estonian Dependency Treebank, an ongoing corpus annotation project. Although the treebank construction is still under way, we have used it for training MaltParser and experimenting with combining MaltParser with a rule-based Constraint Grammar parser for Estonian. MaltParser achieves unlabeled attachment score (UAS; correct links to head node) of 83.4% and label accuracy (LA) of 88.6%. Labeled attachment score (LAS) was 80.3%.