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Spin-half nuclei in a magnetic field possessing a population difference in excess of that expected at thermal equilibrium are said to be hyperpolarised. Dynamic Nuclear Polarisation (DNP) is a method to generate hyperpolarised systems, pumping nuclear spins into a given state at low temperature. Hyperpolarised samples can be rapidly dissolved in a hot solvent, and maintain a highly polarised spin population that relaxes to the new thermal equilibrium over several minutes. It is possible to inject hyperpolarised molecules into an organism, sample the population difference through NMR spectroscopy, and obtain spectra with a large ( > 104) increase in their signal-to-noise ratio compared to thermal equilibrium. The use of hyperpolarised [1-13C]pyruvate allows for the quantification of the rate of [1-13C]lactate production, increases of which are a defining characteristic of cancer; or the rate of 13C-bicarbonate production, which is altered in heart disease. This thesis describes the development of magnetisation-efficient sequences of spectrally-and-spatially selective radiofrequency pulses and rapid imaging readouts that are able to image the metabolism of hyperpolarised [1-13C]pyruvate in three dimensional space, with a reconstructed resolution of 1 x 1 x 2 mm3. The technique's sensitivity to metabolism is demonstrated, and attempts are made to image cancer that has metastasised to the brain prior to the point of conventional detection through its metabolic phenotype. It is also used to image metabolism in the post ischaemic myocardium, where it reports on regions of non-viable tissue. Additionally, hyperpolarised 13C-urea is used as a 'metabolically inert' probe of perfusion in the myocardium. Flow-sensitisation gradients and a spiral readout allow 13C-urea to be resolved in the myocardium. The ability to 'co-polarise' [1-13C]pyruvate and 13C-urea is demonstrated. This technique could simultaneously resolve perfusion deficits and metabolic changes in the acutely damaged heart, with several potential advantages over current clinical methods. Finally, several methods for analysing data generated by hyperpolarised experiments are proposed: weighted averaging for combining spectroscopic data of varying quality; novel Bayesian approaches to quantifying metabolic rate constants of interest following the injection of hyperpolarised [1-13C]pyruvate; and the Fast Padé Transformation as an improved method for the reconstruction of truncated hyperpolarised spectral data. DNP is a technique that, following its development for particle physics experiments in the 1970s, is transitioning to clinical practice as a safe, novel molecular imaging modality. It is hoped that the techniques proposed in this text ultimately find wide utility in the assessment of cancer and heart disease, which combined are responsible for approximately 50% of deaths occurring in the developed world.