Large knowledge bases, the Linked Data cloud, and Web 2.0 communities open up new opportunities for deep question answering to support the advanced information needs of knowledge workers like students, journalists, or business analysts. This calls for going beyond keyword search, towards more expressive ways of entity-relationship-oriented querying with graph constraints or even full-edged languages like SPARQL (over graph-structured, schema-less data). However, a neglected aspect of this active research direction is the need to support also query refinements, relaxations, and interactive exploration, as single-shot queries are often insufficient for the users' tasks. This paper addresses this issue by discussing the paradigm of Iterative Querying, IQ for short. We present two instantiations for IQ, one based on keyword search over labeled graphs combined with structural constraints, and another one based on extensions of the SPARQL language. We discuss the suitability of these approaches for knowledge-centric search tasks, and we identify open research problems that deserve greater attention.