'Going under' and 'staying under' general anesthesia requires a combination of medications. Most of them can still affect your breathing even after you have 'woken up' after your surgery. Someone with obstructive sleep apnea is at risk for serious cardiovascular events and breathing problems after waking up from general anesthesia. The overall risk of a significant event depends on the severity of your sleep apnea. This is the reason that testing for sleep apnea prior to surgery is of significant importance.