Background: Despite proven clinical benefits, only a minority of patients complete outpatient cardiac rehabilitation (CR) after acute myocardial infarction (AMI). The main purpose of this study was to evaluate to what extent and at which time patients drop out of CR, and to assess which patient-related characteristics can predict dropout. Methods: In a retrospective cohort study, we selected patients who had been hospitalised with an AMI in our centre in 2015 or 2016. Patients were selected pseudonymously based on reimbursement codes in the electronic health record. We extracted baseline characteristics and data on CR referral, enrolment and completion for each patient. Multivariable logistic regression was used to assess which characteristics predicted referral and dropout. Results: The 666 patients included were predominantly male (66%), with a mean age of 69.0 years. Of the 640 eligible patients, 201 (31%) were not referred for CR. Enrolment after referral was 94%. Nonreferral was independently associated with older age, female sex, traveling distance, non-ST-elevation myocardial infarction (NSTEMI; as compared with STEMI), no coronary revascularisation and prior manifestations of coronary artery disease. Of the 414 enrolled patients, 24% did not complete their CR programmes (i.e. dropped out). Older age and worse exercise capacity at baseline were independently associated with dropout. The ability of the multiple regression models to predict nonreferral and noncompletion was good to fair, with an area under the receiver operating characteristic curves of 0.86 and 0.71, respectively. Conclusion: The main reason for not participating in or not completing CR after AMI was nonreferral. To optimise CR utilisation, improvement of referral rates should be prioritised.