Most of our knowledge about human visual performance describes foveal vision with a well centered pupil. However, these studies of "on-axis" vision do not provide much insight into the effects of moving the retinal image or the pupil off-axis. In this chapter we define the inherent optical and neural axes of the human eye, and we examine the optical and visual effects of decentering either the retinal image or the entrance pupil. The optical axis of the eye is usually well centered on the eye's neural axis, which provides best image quality at the fovea. Decentration of the eye's entrance pupil can occur when using any visually-coupled electro-optical device with a defined exit pupil. This decentration can lead to reduced light sensitivity, reduced spatial resolution, reduced contrast sensitivity, color distortions, unpredictable changes in refractive error, wavelength-specific distortions of visual direction and wavelength-specific errors in the judgment of apparent depth and size. We then examine associated problem of a centered pupil and an off-axis object and conclude with a simple computational model that accounts for the majority of the effects on contrast sensitivity and spatial resolution.