Statistical language modeling (LM) that purports to quantify the acceptability of a given piece of text has long been an interesting yet challenging research area. In particular, language modeling for information retrieval (IR) has enjoyed remarkable empirical success; one emerging stream of the LM approach for IR is to employ the pseudo-relevance feedback process to enhance the representation of an input query so as to improve retrieval effectiveness. This paper presents a continuation of such a general line of research and the main contribution is threefold. First, we propose a principled framework which can unify the relationships among several widely-used query modeling formulations. Second, on top of the successfully developed framework, we propose an extended query modeling formulation by incorporating critical query- specific information cues to guide the model estimation. Third, we further adopt and formalize such a framework to the speech recognition and summarization tasks. A series of empirical experiments reveal the feasibility of such an LM framework and the performance merits of the deduced models on these two tasks.