Magnetic resonance images may be sensitised to tissue perfusion and oxygenation, providing functional information about organs in the body. These MR techniques are of great value for the assessment of ischaemic conditions, both for clinical diagnosis and to investigate disease processes in animal models. Perfusion may be studied completely non-invasively using arterial spin labelling (ASL) to magnetically label blood. The presence of deoxyhaemoglobin (dHb) influences spin-spin relaxation times, producing blood-oxygen-level-dependent (BOLD) contrast in images. ASL and BOLD MRI are investigated in this thesis in rat brain and liver. Theoretical and practical aspects of labelling blood by velocity driven adiabatic fast passage (AFP) for continuous ASL (CASL) are considered. A computer model of the modified Bloch equations facilitated optimisation of velocity driven AFP under various experimental and physiological conditions in humans and animals. The computer model was extended to investigate the amplitude modulated (AM) control pulse for multiple-slice CASL. The effect of the AM control on moving spins and some of the reasons for the non-ideal performance of the technique are explained. The AM control was implemented and results in rat brain in-vivo demonstrate that the technique is significantly less sensitive to perfusion than the standard control technique for single slice CASL imaging. BOLD was employed in an animal model of intestinal ischaemia- reperfusion (I/R). This is a devastating condition that affects remote organs, including the liver, lungs, heart, kidney and central nervous system, and may lead to multiple-organ-dysfunction-syndrome. BOLD MRI of the liver during intestinal I/R showed that R2* increases throughout reperfusion. This suggests that dHb accumulates in the liver, consistent with the triggering of the failure of hepatic energy metabolism by intestinal reperfusion following ischaemia.