Continuous location-dependent queries can be considered as key elements for the development of different categories of location-based and context-aware services. However, most work on location-dependent query processing has been mainly oriented towards outdoor environments. This paper studies location-dependent and context-aware queries over moving objects in indoor environments (e.g., houses, commercial malls, etc.), with a special focus on navigation-related queries (i.e., mainly path search and range queries). A hierarchical and context-dependent spatial data model is firstly presented, which leads to the consideration of other contextual dimensions besides the location of the involved entities, such as time and user profiles. Two algorithms for continuous processing of path and range queries on top of this modelling approach are introduced. The former performs a hierarchical and incremental path search for the continuous processing of path queries, and applied to both static and moving objects. The latter presents an incremental approach for continuous range queries, which performs a hierarchical network expansion around the initial query point and implements a mechanism to update the initial search tree based on user's movements.