Understanding how designers think is core to advancing design methods, tools, and outcomes. Engineering researchers have effectively turned to cognitive science approaches to studying the engineering design process. Empirical methods used for studying designer thinking have included verbal protocols, case studies, and controlled experiments. Studies have looked at the role of design methods, strategies, tools, environment, experience, and group dynamics. Early empirical studies were casual and exploratory with loosely defined objectives and informal analysis methods. Current studies have become more formal, factor controlled, aiming at hypothesis testing, using statistical design of experiments (DOE) and analysis methods such as analysis of variations (ANOVA). Popular pursuits include comparison of experts and novices, identifying and overcoming fixation, role of analogies, effectiveness of ideation methods, and other various tools. This paper first reviews a snapshot of the different approaches to study designers and their processes. Once the current basis is established, the paper explores directions for future or expanded research in this rich and critical area of designer thinking. A variety of data may be collected, and related to both the process and the outcome (designs). But there are still no standards for designing, collecting and analyzing data, partly due to the lack of cognitive models and theories of designer thinking. Data analysis is tedious and the rate of discoveries has been slow. Future studies may need to develop computer based data collection and automated analyses, which may facilitate collection of massive amounts of data with the potential of rapid advancement of the rate of discoveries and development of designer thinking cognitive models. The purpose of this paper is to provide a roadmap to the vast literature for the benefit of new researchers, and also a retrospective for the community.