This is a multi-site, open- label rollover study to evaluate the long-term safety and efficacy of CTX001 in pediatric and adult participants who received CTX001 in parent studies 111 (NCT03655678) 141 (NCT05356195) or 161 (NCT05477563) (transfusion-dependent β-thalassemia \[TDT\] studies) or Study 121 (NCT03745287) or 151 (NCT05329649) or 161(NCT05477563) (severe sickle cell disease \[SCD\] studies).