This paper focuses on the effect of the drill geometry on the drilling of woven Carbon Fiber Reinforced Polymer composite (CFRPs). Although different geometrical effects can be considered in drilling CFRPs, the present work focuses on the influence of point angle and wear because they are the important factors influencing hole quality and machining forces. Surface quality was evaluated in terms of delamination and superficial defects. Three different point angles were tested representative of the geometries commonly used in the industry. Two wear modes were considered, being representative of the wear patterns commonly observed when drilling CFRPs: flank wear and honed cutting edge. It was found that the crossed influence of the point angle and wear were significant to the thrust force. Delamination at the hole entry and exit showed opposite trends with the change of geometry. Also, cutting parameters were checked showing the feed's dominant influence on surface damage.