Conventional spatial queries are usually meaningless in dynamic environments since their results may be invalidated as soon as the query or data objects move. In this paper we formulate two novel query types, time parameterized and continuous queries , applicable in such environments. A time-parameterized query retrieves the actual result at the time when the query is issued, the expiry time of the result given the current motion of the query and database objects, and the change that causes the expiration. A continuous query retrieves tuples of the form < result , interval >, where each result is accompanied by a future interval , during which it is valid. We study time-parameterized and continuous versions of the most common spatial queries (i.e., window queries, nearest neighbors, spatial joins), proposing efficient processing algorithms and accurate cost models.