A shaving apparatus 1000 is disclosed in which a rotary cutter 130 and a blade 250 are used to shear a user's hairs therebetween during a shaving process. Various advancements are disclosed herein, including without limitation accurate positioning of the blade relative to the rotary cutter, pivoting of a refill blade assembly 200 relative to a base portion 100 of the shaving apparatus to which it is coupled, and a connection between the refill blade assembly and the base portion of the shaving apparatus. Furthermore, a method of shaving is also disclosed.