Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education. This development is a welcome one for those interested in the topic, but also poses a challenge, especially to teachers and new scholars. It has become more and more difficult to get an overview of the field and to identify the key concepts used in research on proof and proving. This book is intended to help teachers, researchers and graduate students to overcome the difficulty of getting an overview of research on proof and proving. It reviews the key findings and concepts in research on proof and proving, and embeds them in a contextual frame that allows the reader to make sense of the sometimes contradictory statements found in the literature. It also provides examples from current research that explore how larger patterns in reasoning and argumentation provide insight into teaching and learning.