Summary: This thesis attempts to contribute with some novel numerical methods in applied superconductivity, including a comprehensive discussion of the different mechanism involved in the vortex dynamics, as well as some relevant microscopic phenomena. The book has been structured in three parts. On the one hand, a general critical state theory for type-II superconductors with magnetic anisotropy, its computation, implications, and consequently some applications for particular problems, is what the first and second part try to convey. On the other hand, some microscopical aspects of the superconductivity have been also considered and the attained results have been compiled along the third part of this thesis. Resumen: Esta tesis aporta nuevos métodos numéricos en superconductividad aplicada, incluyendo una amplia discusión de los diferentes mecanismos involucrados en la dinámica de vórtices, así como de algunos fenómenos microscópicos relevantes. En las partes I y II se presenta una teoría general del estado crítico para superconductores tipo-II con anisotropía magnética, así como su aplicación a varios problemas concretos mediante cálculos numéricos específicos. En la parte III han sido considerados algunos aspectos microscópicos de la superconductividad.