The work presented in the following pages deals with certain aspects of the current algebraic approach to the problem of broken symmetries in the theory of elementary particles (Chapter 1) and related considerations arising from the attempts to understand the situation in field theoretic terms (Chapter 2). In the final chapter we are concerned mainly with an investigation Into the possible superconvergence relations for pion photoproduction off nucleons through a study of the known Regge trajectories arising in the u-channel, Such relations have recently attracted considerable interest because of their relevance to the elucidation of higher symmetry schemes and the algebra of currents. The work contained in Sections 7--15, Chapter 1; Sections 5-6 Chapter 2; Sections 4-5,. Chapter 3 is original.