This PhD thesis proposal is focused on proposing solutions to the problem of Partial Shape Retrieval which is part of the Three-Dimensional Object Retrieval problem and represents a very challenging problem. Given a shape (or a part of a shape) as query, one wants to retrieve from a collection of 3D models those objects which contain parts visually similar to the query. Difficulties can arise due to the need of representing a model in a compact way with local information, where the extent of the locality is unknown a priori. In addition, the matching becomes an expensive task because of the large amount of possible memberships of the partial query in the shapes. Typically, assumptions are made to constrain the problem in order to solve it effectively. Therefore, partial shape retrieval is a challenging and open problem. In this document, we provide proposals to address this problem and furthermore, we discuss the open problems and the important issues that should be tackled in order to solve the problem of Partial Shape Matching and Retrieval. Copyright 2011 ACM.