The purpose of this work is to defend the revival of coroutines as a powerful and convenient control construct, which can replace both firstclass continuations and threads with a single and simpler concept. In order to provide an adequate and precise definition of the concept of coroutines, we propose a new classifying system, and introduce the concept of complete coroutines, for which we provide a formal definition based on an operational semantics. We then demostrate that complete symmetric coroutines and complete asymmetric coroutines have equivalent expressive power, as well as complete coroutines and one-shot traditional and partial continuations. We also discuss the advantages of using complete asymmetric coroutines instead of symmetric coroutines or first-class continuations. Finally, we analyse the benefits and problems associated with different concurrency models, and argue in favor of the replacement of multithreading with alternative concurrency models and the provision of coroutines as a basic concurrency construct, adequate for the implementation of these alternative models.