Background: Aphasia following stroke refers to impairments that affect the comprehension and expression of spoken and/or written language, and co‐occurring cognitive deficits are common. In this paper we focus on short‐term and working memory impairments that impact on the ability to retain and manipulate auditory–verbal information. Evidence from diverse paradigms (large group studies, case studies) report close links between short‐term/working memory and language functioning in aphasia. This evidence leads to the hypothesis that treating such memory impairments would improve language functioning. This link has only recently been acknowledged in aphasia treatment but has not been embraced widely by clinicians. Aims: To examine the association between language, and short‐term and working memory impairments in aphasia. To describe practical ways of assessing short‐term and working memory functioning that could be used in clinical practice. To discuss and critically appraise treatments of short‐term and working memory reported in the literature. Methods & Procedures: Taking a translational research approach, this paper provides clinicians with current evidence from the literature and practical information on how to assess and treat short‐term and working memory impairments in people with aphasia. Published treatments of short‐term and/or working memory in post‐stroke aphasia are discussed through a narrative review. Main Contributions: This paper provides the following. A theoretical rationale for adopting short‐term and working memory treatments in aphasia. It highlights issues in differentially diagnosing between short‐term, working memory disorders and other concomitant impairments, e.g. apraxia of speech. It describes short‐term and working memory assessments with practical considerations for use with people with aphasia. It also offers a description of published treatments in terms of participants, treatments and outcomes. Finally, it critically appraises the current evidence base relating to the treatment of short‐term and working memory treatments. Conclusions: The links between short‐term/working memory functioning and language in aphasia are generally acknowledged. These strongly indicate the need to incorporate assessment of short‐term/working memory functioning for people with aphasia. While the supportive evidence for treatment is growing and appears to highlight the benefits of including short‐term/working memory in aphasia treatment, the quality of the evidence in its current state is poor. However, because of the clinical needs of people with aphasia and the prevalence of short‐term/working memory impairments, incorporating related treatments through practice‐based evidence is advocated.