In this thesis, different aspects of the physics of flows in the solar atmosphere are examined. These are described by means of the set of (ideal) magnetohydrodynamics (MHD) and throughout the thesis there is a progressive refinement in the mathematical methods to solve these equations. First, an analysis of symmetric MHD equilibria is presented and the difficulties that are found in solving the steady equations, both analytically and numerically, are discussed in detail. A novel method to find exact solutions in the incompressible case is presented and families of solutions are given in different geometries. Then, attention is turned to flows in coronal magnetic structures, namely quiescent prominences (closed fieldlines) and polar plumes (open fieldlines), and MHD models for these structures are developed by following two different methods: for the former a semi- analytic approach while for the latter a linearisation through a low β assumption. In the prominence model, the effects of a subsonic flow along the fieldlines supporting the structure are studied and the results are compared both with a previous static model and with the observed flow speeds. For the plume model, flows are supposed to be transonic along the open fieldlines and their behaviour is studied for different distributions of temperature, density and magnetic flux. However, here the main goal is to demonstrate that coronal plumes are essentially magnetic features and some results of the model are compared with observations. Finally, a time dependent MHD code in spherical coordinates is presented. The aim is to study the interaction of the solar wind with the large scale coronal magnetic structures and the propagation of MHD waves. As a test in 1-D, simulations of the dynamic response of a spherically symmetric extended corona to changes at the outer pressure are studied, following a previous analytic work.