In this paper, we offer a comparative review of research on understanding and promoting students' mathematical thinking. The sources for the review are papers that were published in "Educational Studies in Mathematics" ("ESM") during two windows of time: 1994-1998 and 2014-2018. Selection of these two time periods enables us to comment on the "state of the art" in research as well as identify changes over the past 25 years. The review is guided by an analysis of conceptualizations of "mathematical thinking" proposed in the research literature, selected curriculum documents, and international assessment programs such as the OECD's Programme for International Student Assessment (PISA). The review not only documents salient features of research studies, such as the country of origin of the authors, educational level of the participants, research aims, theoretical perspectives, and methodological approaches, but also identifies the contribution to knowledge made by this body of work as well as future research directions and opportunities.