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We attempt a brief and broad overview and historical perspective of the theory of lightwave propagation in dielectric waveguides. This is a subject that is now documented by extensive literature. As our review task is limited by constraints in both space and time it will be illustrative rather than comprehensive. The illustrations are intended to highlight the principal concepts and theoretical approaches and refer the reader to the literature for detailed derivations and explanations. Our story celebrates a theory with a proud history of nearly 100 years, vibrant and rich in new ideas, and serving as the base for an increasing number of powerful applications.