The requirement for deoxygenation in controlled/living radical polymerisation (CLRP) places significant limitations on its widespread implementation by necessitating the use of large reaction volumes, sealed reaction vessels as well as requiring access to specialised equipment such as a glove box and/or inert gas source. As a result, in recent years there has been intense interest in developing strategies for overcoming the effects of oxygen inhibition in CLRP and therefore remove the necessity for deoxygenation. In this review, we highlight several strategies for achieving oxygen tolerant CLRP including: "polymerising through" oxygen, enzyme mediated deoxygenation and the continuous regeneration of a redox-active catalyst. In order to provide further clarity to the field, we also establish some basic parameters for evaluating the degree of "oxygen tolerance" that can be achieved using a given oxygen scrubbing strategy. Finally, we propose some applications that could most benefit from the implementation of oxygen tolerant CLRP and provide a perspective on the future direction of this field.