Risk analyses have been used in the Norwegian offshore petroleum industry for more than two decades. The analyses have been closely linked to the use of risk acceptance criteria (RAC). This paper gives a short review of the motivation and use of RAC in the management of risk at offshore installations. Focus is on the present situation and challenges in the Norwegian petroleum industry. The paper will discuss some recommended principles for arriving at risk acceptance. The relation between the acceptability of risk and the cost-benefit of risk reducing measures is also considered, mainly in the context of the ALARP (As Low As Reasonably Practicable) principle.