Visualization exploration is the process of extracting insight from data via interaction with visual depictions of that data. Visualization exploration is more than presentation; the interaction with both the data and its depiction is as important as the data and depiction itself. Previous visualization research has focused on the generation of visualizations---the depiction---and not on the exploratory aspects of the visualization process. However, without user interfaces for and formal models of the visualization process, visualization exploration sessions cannot be fully utilized. Towards this end, this dissertation introduces a model and framework for the visualization exploration process. This research aims at providing a framework for capturing, representing, and manipulating information derived during the visualization discovery processes in a systematic manner. In particular, this work focuses on the exploration during the data analysis and visualization process through the use of intuitive graphical user interfaces. These interfaces provide a structured environment for the exploration of the visualization parameter space. The interfaces utilize a formal model of the visualization process that captures the fundamental operations performed during this exploration. The model is independent of the visualization performed or user interface utilized. In addition, instances of the model can be shared between users via an interoperable representation format. The goal of this work is to maximize user productivity by offering them an effective mechanism to fetch, edit, reuse, and share with others their visualizations which may include raw data, data associations, visualization results, and the steps taken to derive the visualization results.