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In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion systems of equations, and how they behave when subject to symmetry breaking perturbations. We present an asymptotic theory of the study of meandering (quasiperiodic spiral wave solutions) spiral waves which are drifting due to symmetry breaking perturbations. This theory is based on earlier theories: the 1995 Biktashev et al theory of drift of rigidly rotating spirals, and the 1996 Biktashev et alarXiv:0912.4247v1 fatcat:t7wfdyvlwzhy7pr5j6qfyolsza