We start with a brief review of evidence that verbal working memory (WM) involves a limited capacity phonological loop capable of retaining verbal sequences for a few seconds in immediate serial recall, vocabulary acquisition, speech production and language comprehension. The challenge of explaining how such a system handles information about serial order is discussed in the context of computational models of the immediate recall of unstructured sequences of words, letters, or digits, an extensively studied laboratory task for which there are many benchmark findings. Evaluating computational models against these benchmarks suggests a serial ordering mechanism in which items are simultaneously active before being selected for sequential output by a process of competitive queuing (CQ). Further evidence shows how this process may operate in the context of sequences that conform to various kinds of linguistic constraint. We conclude by suggesting that CQ is a promising theoretical mechanism for connecting and potentially unifying theories of WM and language processing more generally despite major differences in their scope and level of abstraction.