Flow in a rapidly rotating, precessing spherical shell is studied with and without an applied magnetic dipole field in order to model the Earth's core. The primary response of the fluid to precessional forcing is a solid body rotation about an axis other than the rotation axis of the shell. The orientation and energy of that flow is predicted well by an asymptotic theory. Ekman layers at the boundaries of the shell break down at critical latitudes and spawn internal shear layers. The limit of small precession rate is investigated in particular: at zero magnetic field, the strongest shear layers are inclined at 30° with respect to the rotation axis of the shell and erupt at 30° latitude from the inner core. When a magnetic dipole field with its dipole oriented along the rotation axis of the shell is applied, shear zones develop additional structure and change position and orientation. At an Elsasser number of 10, most flow structures tend to align with the rotation axis of the shell.