Visualization has proved to be a suitable paradigm for the analysis and exploration of datasets. In the data mining cycle, visualization has been mainly focused on data visualization and output generation. However, besides datasets, many other entities need to be explored and understood by users and analysts. In this paper, we describe the role of visualization in the data mining process, and we present a model to support the interaction between users and data mining entities. We discuss visualizations of datasets, parameter spaces of data mining algorithms, models induced from datasets, and patterns generated by the application of data mining algorithms to datasets. We have developed a Java-based testbed, that implements the extended data mining model with visual support to interact with datasets, models, parameter spaces, and patterns. Experimental results based on several public datasets, data mining algorithms, multidimensional visualization techniques, and other novel visualizations, show clearly the benefits of the integration of visualization in the data mining process.