For several decades, quasi-periodic pulsations (QPP) in flares have been a signature feature of solar dynamics. In the last fifteen years, the advent of new observational instruments has led to a much-improved scope for studying and understanding such phenomena. These events are particularly relevant to the field of coronal seismology, where impulsive events are used as diagnostic tools to estimate the physical parameters of the solar atmosphere remotely. \ud In this thesis we investigate quasi-periodic pulsations in flares from both a numerical and observational perpective, mostly in terms of magnetohydrodynamic (MHD) waves. It has long been suggested that MHD modes may be the cause of QPP in flares as they are capable of modulating a wide range of observable quantities. We study one such mode in detail: the sausage mode. For a model including significant gas pressure, the characteristic period, the ratio of the mode harmonics and the behaviour of the wavenumber cutoff are all considered. Although the period and wavenumber are only marginally affected by this gas pressure, the density contrast ratio and length are important factors. An observational study of a flaring QPP event was undertaken, where new techniques were developed in an attempt to successfully diagnose the QPP mechanism. \ud Cross-correlation mapping was applied to spatially resolved radio data, showing how the strength and phase relationship of a flaring oscillation can be mapped in space. Using this information, we were able to exclude many mechanisms as possible drivers for this event, and suggest that an MHD sausage mode is the likely candidate. \ud A second flaring QPP event was considered, based on the possibility of multiple harmonic oscillations. A sequential spectral peak filtering method was used to demonstrate the presence of multiple significant periods in the flare. Analysis of the harmonic ratios indicated that an MHD wave such as a kink mode was the probable cause. \ud Finally we explore the potential of a new technique in the context of the solar corona, the combination of empirical mode decomposition (EMD) and the Hilbert spectrum. It was established that, under certain circumstances, this method compared favourably with existing analysis techniques such as the Morlet wavelet, and may lead to significant future observational results
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