We develop a theoretical framework that formalizes the conflicts of interest arising in continuation vehicles (CVs), in which general partners (GPs) transfer portfolio companies from an existing fund to a new vehicle they continue to manage. While CVs can enhance efficiency by extending the holding period of high-potential firms, they also create opportunities for rent extraction as GPs can exploit their informational advantage and intermediary position between legacy and new limited partners (LPs). CV formation involves two informational frictions: adverse selection, whereby new LPs overpay for low-quality assets, and inverse selection, whereby they underpay for high-quality assets. We show that the likelihood and performance of CVs depend on GP coinvestment and carried interest incentives, as well as on whether the legacy fund is in or out of the money. The model links LP liquidity needs, GP incentives, and contract design to CV performance and the distribution of value across investors. Using proprietary data on continuation vehicle transactions, we also provide systematic evidence on contractual features in these deals that has not previously been documented.