  We study global aspects of N=2 Kazama-Suzuki coset models by investigating
topological G/H Kazama-Suzuki models in a Lagrangian framework based on gauged
Wess-Zumino-Witten models. We first generalize Witten's analysis of the
holomorphic factorization of bosonic G/H models to models with N=1 and N=2
supersymmetry. We also find some new anomaly-free and supersymmetric models
based on non-diagonal embeddings of the gauge group. We then explain the basic
properties (action, symmetries, metric independence, ...) of the topologically
twisted G/H Kazama-Suzuki models. We explain how all of the above generalizes
to non-trivial gauge bundles.
  We employ the path integral methods of localization and abelianization (shown
to be valid also for non-trivial bundles) to establish that the twisted G/H
models can be localized to bosonic H/H models (with certain quantum
corrections), and can hence be reduced to an Abelian bosonic T/T model, T a
maximal torus of H. We also present the action and the symmetries of the
coupling of these models to topological gravity. We determine the bosonic
observables for all the models based on classical flag manifolds and the
bosonic observables and their fermionic descendants for models based on complex
Grassmannians.
