This thesis is an account of various phenomena caused by the interaction of the motion of electrically conducting fluids with magnetic fields. Such phenomena, the study of which is usually known as Magnetohydrodynamics (MHD), occur on a galactic, planetary or laboratory length scale; however in this thesis we concentrate on those phenomena which can be reproduced in the laboratory. In chapter 2 we study the laminar flow of uniformly conducting, incompressible fluids in rectangular ducts under the action of transverse magnetic fields. We begin by proving that when the duct has a constant cross-section the solution is unique and then analyse theoretically some of the curious effects on the flow of the duct's walls being electrically conducting. We find close agreement between the results of these theories and the experiments of Alty (1966) and Baylis (1966). We then analyse the flow in ducts with varying cross-sections. In chapter 3 we analyse some of the curious flows and current streamline patterns produced by placing electrodes on the non-conducting walls of a container, filled with a conducting fluid, and passing electric currents between the electrodes in the presence of a strong magnetic field. In chapter 4 we analyse some of the theoretical limitations on the use of Pitot tubes and electric potential (e.p.) probes in MHD flows, and provide some estimates of the errors to be expected. In chapter 5 we analyse the stability of parallel flows in parallel magnetic fields and also some aspects of the stability of the flows analysed in chapters 2 and 3. In chapters 6, 7 and 8 we describe our experimental apparatus, the experiments to investigate directly some of the flows analysed theoretically in chapters 2 and 3 by means of Pitot and e.p. probes, and experiments to measure the MHD errors inherent in the use of these probes. We concluded that the curious phenomena predicted actually exist. We also learnt much about the use of Pitot and e.p. probes, especially as some of the experimental results were as predicted in chapter 4.