The term “magnetosphere” originated historically from early spacecraft measurements of plasma trapped by the magnetic field of earth and other planets. But over the years this concept has also been applied to the magnetically channeled wind outflows from magnetic stars. The review here describes the basic magnetohydrodynamics (MHD) approach used to model such stellar magnetospheres, with emphasis on the central competition between confinement by the magnetic field vs.expansion of the stellar wind outflow. A key result is that, for a star with a dipole surface field B∗, surface radius R∗, and asymptotic wind momentum ${\dot M} v_{\infty}$, this competition can be well characterized by a single “wind magnetic confinement parameter”, $\eta_{\ast} \equiv B_{\ast}^{2} R_{\ast}^{2}/{\dot M} v_{\infty}$. For large η∗, closed magnetic looops can confine parts of the wind up to an Alfvén radius RA ≈ η1/4R∗, leading to “magnetically confined wind shocks” that might produce the relatively hard X-ray emission seen in some magnetic stars. In rotating stars, RA also roughly characterizes the radius up to which material co-rotates with the underlying star. For the outflowing wind, the associated loss of angular momentum, can lead to spindown in the stellar rotation over a time much shorter than the star's evolutionary timescale. For confined material within RA but beyond the star's Keplerian corotation radius RK, the net centrifugal support against gravity can lead to a “rigidly rotating magnetosphere” composed of accumulating trapped wind. This can provide a natural explanation for the rotationally modulated Balmer line emission observed from magnetic Bp stars. Moreover, magnetic reconnection heating from episodic centrifugal breakout events might explain the occasional very hard X-ray flares seen from such stars. Overall, it seems clear that magnetic fields can play a strong role in confining and channeling such stellar wind outflows, providing a natural explanation for various observational signatures structure and variability in the winds and circumstellar envelopes of massive stars.