ABSTRACT Cognitive deficits beyond language may be present in aphasia, and accurately assessing them is fundamental for treatment planning. However, it is unclear which tools are currently used to assess cognition in aphasia, how much language they require, and which cognitive domains should be the focus of assessment. This study aimed to determine which cognitive domains have been the focus of assessment, and systematically appraise the linguistic requirements of these tests. We followed the PRISMA-ScR guidelines and systematically searched the literature from 2010–2020 for the tests used to assess cognition in research with people with aphasia. 480 studies were included and 389 tests were appraised for their linguistic load. Results showed that cognitive testing focused mostly on executive functions and memory. Over half the tests used to assess cognition in aphasia had some degree of language load (i.e., verbal stimuli, language production or required mapping stimuli to its meaning). This review highlights the difficulty in accurately diagnosing concomitant cognitive deficits in aphasia due to the language requirements in commonly used cognitive assessments. This review underlines the need to be mindful of the linguistic requirements in cognitive assessments. Finally, we offer some recommendations of which tests may be the most appropriate to assess cognition in aphasia.