Objectives Neurocognitive deficits are central in schizophrenia. Cognitive remediation has proven effective in alleviating these deficits, with medium effect sizes. However, sizeable attrition rates are reported, with the reasons still uncertain. Furthermore, cognitive remediation is not part of routine mental health care. We conducted a systematic review to investigate factors that influence access and engagement of cognitive remediation in schizophrenia. Methods We systematically searched the PubMed, Web of Science, and PsycINFO databases for peer-reviewed articles including a cognitive remediation arm, access, and engagement data, and participants with schizophrenia spectrum disorders aged 17–65 years old. Duplicates and studies without a distinct cognitive remediation component, protocol papers, single case studies, case series, and reviews/meta-analyses were excluded. Results We included 67 studies that reported data on access and engagement, and extracted quantitative and qualitative data. Access data were limited, with most interventions delivered on-site, to outpatients, and in middle- to high-income countries. We found a median dropout rate of 14.29%. Only a small number of studies explored differences between dropouts and completers ( n = 5), and engagement factors ( n = 13). Dropouts had higher negative symptomatology and baseline self-efficacy, and lower baseline neurocognitive functioning and intrinsic motivation compared to completers. The engagement was positively associated with intrinsic motivation, self-efficacy, perceived usefulness, educational level, premorbid intelligence quotient, baseline neurocognitive functioning, some neurocognitive outcomes, and therapeutic alliance; and negatively associated with subjective cognitive complaints. Qualitative results showed good acceptability of cognitive remediation, with some areas for improvement. Conclusions Overall, access and engagement results are scarce and heterogeneous. Further investigations of cognitive remediation for inpatients, as well as remote delivery, are needed. Future clinical trials should systematically explore attrition and related factors. Determining influential factors of access and engagement will help improve the implementation and efficacy of cognitive remediation, and thus the recovery of people with schizophrenia.