The transaction concept provides a central paradigm for correctly synchronizing concurrent activities and for achieving reliability in database systems. In transaction modeling and processing, theory and practice influence each other a lot, and over the years the transaction concept has undergone a considerable evolution from a pure implementation vehicle to a powerful abstraction concept. This survey deals with conceptual issues in designing transaction models, and with approaches to specify correctness of concurrent transaction executions (schedules). As will be described, there is a vastly uniform methodology for putting these aspects to work, which is illustrated by examples ranging from simple reads and writes to semantically rich operations. In addition, the survey covers novel transaction models, whose goal is to adequately support a variety of requirements arising in modern database applications.