  In the first part of this thesis I study the intermediate regime between
ordinary lasing and a BEC of exciton polaritons. I take into account the
fermionic structure of polaritons, treating the excitons as two-level systems
coupled to a single mode in a microcavity. I introduce decoherence and
dissipation processes to this system. Employing many-body Green function
techniques, similar to those used by Abrikosov and Gor'kov in their theory of
gapless superconductivity, I provide a mathematical structure that unifies
models of lasers with models of condensates. This allows me to study the
stability of the polariton condensate with respect to decoherence processes and
the crossover between the polariton condensate and the laser. I give detailed
indications of a regime in which the condensate should be observed to guide
experimental work and show how to distinguish the Bose condensate from a laser.
  The second part of this thesis is concerned with properties of excitons and
modelling of excitonic lasing in quasi-one-dimensional quantum wires. I develop
a very general numerical method of calculating the properties of wires with
different shapes and materials. Using this method I study the properties of
very wide range of T-shaped quantum wires.
