Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. The generality of the approach provides a wide application area ranging from philosophy to computer science. This book gives a comprehensive survey of logical research within and around arrow logic. Since the natural operations on transitions include composition, inverse and identity, we can study their logic--arrow logic--from two different perspectives, and by two (complementary) methodologies: modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tages. They show what the prices of desirable properties, such as decidability, (finite) axiomatizability, Craig interpolation property, Beth definability etc. are in terms of semantic properties of the logic. The book will benefit researchers with an interest in modal logic and relation algebra.