Recovery from aphasia is thought to depend on neural plasticity, that is, the functional reorganization of surviving brain regions such that they take on new or expanded roles in language processing. We carried out a systematic review and meta-analysis of all articles published between 1995 and early 2020 that have described functional imaging studies of six or more individuals with post-stroke aphasia, and have reported analyses bearing on neuroplasticity of language processing. Each study was characterized and appraised in detail, with particular attention to three critically important methodological issues: task performance confounds, contrast validity, and correction for multiple comparisons. We identified 86 studies describing a total of 561 relevant analyses. We found that methodological limitations related to task performance confounds, contrast validity, and correction for multiple comparisons have been pervasive. Only a few claims about language processing in individuals with aphasia are strongly supported by the extant literature: First, left hemisphere language regions are less activated in individuals with aphasia than in neurologically normal controls; and second, in cohorts with aphasia, activity in left hemisphere language regions, and possibly a temporal lobe region in the right hemisphere, is positively correlated with language function. There is modest, equivocal evidence for the claim that individuals with aphasia differentially recruit right hemisphere homotopic regions, but no compelling evidence for differential recruitment of additional left hemisphere regions or domain-general networks. There is modest evidence that left hemisphere language regions return to function over time, but no compelling longitudinal evidence for dynamic reorganization of the language network.