We theoretically investigate tunneling magnetoresistance (TMR) devices, which are probing the spin-momentum coupled nature of surface states of the three-dimensional topological insulator Bi$_{2}$Se$_{3}$. Theoretical calculations are performed based on a realistic tight-binding model for Bi$_{2}$Se$_{3}$. We study both three dimensional devices, which exploit the surface states of Bi$_{2}$Se$_{3}$, as well as two-dimensional devices, which exploit the edge states of thin Bi$_{2}$Se$_{3}$ strips. We demonstrate that the material properties of Bi$_{2}$Se$_{3}$ allow a TMR ratio at room temperature of the order of 1000%. Analytical formulas are derived that allow a quick estimate of the achievable TMR ratio in these devices. The devices can be used to measure the spin polarization of the topological surface states as an alternative to spin-ARPES. Unlike TMR devices based on magnetic tunnel junctions the present devices avoid the use of a second ferromagnetic electrode whose magnetization needs to be pinned.
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