It is commonly claimed in the discussions about the teaching and learning of linear algebra that linear algebra courses are badly designed and badly taught, and that no matter how it is taught, linear algebra remains a cognitively and conceptually difficult subject. This leads to (a) curricular reform actions, (b) analyzing the sources of students' difficulties and their nature, as well as (c) research based and controlled teaching experiments. This chapter is organized along these three axes of action and research. The chapter does not claim the title of an exhaustive review of research on the teaching and learning of linear algebra at the undergraduate level. All omissions should be blamed on the authors' ignorance rather than their bad will.