After a discussion of pre-relativistic conceptions of the present and the Doppler effect, I discuss various notions of the present in the light of the relativity of simultaneity of the Special Theory. Rejecting notions of the present as relative to the observer's inertial frame, or as consisting only in a point of spacetime, I argue that what are compresent to a given process from a and b are all those processes contained within a region of spacetime after a and before b.