In this work I develop a formalization (M-L) of Martin-Löf type theory, the main concern being an accurate definition of what it is to be a model of M-L. Using this definition, I proceed with actual models of M-L (mainly realizability models) to establish the relative consistency of many intuitionistic principles. In addition to their consistency I investigate their interrelationship. The strongest principles which are shown to be consistent with M-L are Church's Thesis and the Fan Theorem. The expressive power of M-L is used to formalize certain theories. The Theory of Real Numbers, an Intuitionistic Set Theory and Category Theory are all formalizable. The constructions of the latter are used to describe Kripke Models of M-L. Finally, I prove that the subsystem of M-L obtained by dropping the rules for cartesian products of types and without rules for universes of types has proof theoretic ordinal ωω
