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We address the problem of querying probabilistic semistructured databases in view of the tradeoff between the efficiency of evaluation and the ability to model probabilistic dependencies between elements of the tree. We introduce, through a discussion of several challenges, the ProApproX query processor over probabilistic XML as a first step towards building a full-fletched probabilistic semistructured data management system. ProApproX aims at efficient data querying of a comparatively larger subset of the XPath query language than was processed by related systems, through techniques of exact calculations or efficient approximations of the result probability. This paper describes PhD work carried out at Telecom ParisTech under the guidance of Pierre Senellart.