In my long-term research program I attempt to develop the Boolean map theory as a general framework for understanding visual attentional processing. This theory starts with a set of Iparsimonious principles (the data format of a Boolean map and a few principles on how it is created) but has implications for a range of attention-related processes. The Boolean map theory has made some progress on previous theories (e.g., feature integration theory) by clarifying the selection/access distinction, offering a clear solution to the access issue, and going beyond the visual search task.