In this dissertation we consider the dynamics of the solar interior, with particular focus on angular momentum balance and magnetic field confinement within the tachocline. In Part I we review current knowledge of the Sun's rotation. We summarise the main mechanisms by which angular momentum is transported within the Sun, and discuss the difficulties in reconciling the observed uniform rotation of the radiative interior with purely hydrodynamical theories. Following Gough & McIntyre (1998) we conclude that a global-scale interior magnetic field provides the most plausible explanation for the observed uniform rotation, provided that it is confined within the tachocline. We discuss potential mechanisms for magnetic field confinement, assuming that the field has a roughly axial-dipolar structure. In particular, we argue that the field is confined, in high latitudes, by a laminar downwelling flow driven by turbulence in the tachocline and convection zone above. In Part II we describe how the magnetic confinement picture is affected by the presence of compositional stratification in the "helium settling layer" below the convection zone. We use scaling arguments to estimate the rate at which the settling layer forms, and verify our predictions with a simple numerical model. We discuss the implications for lithium depletion in the convection zone. In Part III we present numerical results showing how the Sun's interior magnetic field can be confined, in the polar regions, while maintaining uniform rotation within the radiative envelope. These results come from solving the full, nonlinear equations numerically. We also show how these results can be understood in terms of a reduced, analytical model that is asymptotically valid in the parameter regime of relevance to the solar tachocline. In Part IV we discuss how our high-latitude model can be extended to a global model of magnetic confinement within the tachocline.