  We provide a brief characterization of the main features of the homogeneous
sine-Gordon models and discuss a general construction principle for colour
valued S-matrices, associated to a pair of simply laced Lie algebras, which
contain the homogeneous sine-Gordon models as a subclass. We give a brief
introduction to the thermodynamic Bethe ansatz and the form factor approach and
discuss explicit solutions for both methods related to the homogeneous
Sine-Gordon models and its generalization.
