This chapter is written with students in mind. It introduces and describes a problem-oriented multiple perspective approach to history of mathematics, which is a methodology to history of mathematics that is based on an action-oriented conception of history. It is explained how this approach is an open approach to history of mathematics in the sense that the research is driven by a question-answer strategy where the decisive factors for the development have not been decided beforehand, and it is clarified in what sense this approach moves beyond the internal/external division in the historiography of mathematics. The approach is illustrated by three examples from the history of twentieth century mathematics. The first is focused on the invention of the concept of a general convex body, and is a case that can be seen as an exemplar of the move of mathematics into an autonomous enterprise, which is an aspect of the twentieth century mathematics. The second case is concerned with the influence of WWII in the development of mathematical programming. It is an example of how conditions, or urgencies, in society might influence the development of mathematics together with more internal motivated driving forces. The third example deals with Nicolas Rashevsky’s early development of mathematical biology. This case demonstrates how conditions within the sciences, and in society, have a significant influence on what kind of research is being developed, and how mathematical modelling can function as a research tool at the frontier of science. As such, the chapter is an attempt to lay out, present and explain the theoretical perspective and methodology for a problem-oriented multiple perspective approach to history of mathematics and illustrate its strengths and versatility through the three examples.