The term Morphologically Rich Languages (MRLs) refers to languages in which significant information concerning syntactic units and relations is expressed at word-level. There is ample evidence that the application of readily available statistical parsing models to such languages is susceptible to serious performance degradation. The first workshop on statistical parsing of MRLs hosts a variety of contributions which show that despite language-specific idiosyncrasies, the problems associated with parsing MRLs cut across languages and parsing frameworks. In this paper we review the current state-of-affairs with respect to parsing MRLs and point out central challenges. We synthesize the contributions of researchers working on parsing Arabic, Basque, French, German, Hebrew, Hindi and Korean to point out shared solutions across languages. The overarching analysis suggests itself as a source of directions for future investigations.