The goal of this thesis was to study several representatives of conformal sigma models in two-dimensions which possess a continuous symmetry and go beyond the traditional framework, established by the research of last decades in the domain of conformal field theories, of Wess-Zumino-Witten sigma models and of Gaussian models. The sigma models on symmetric superspaces, defined by the standard metric action, provide such examples. The difficulty to solve these sigma models is related to the absence of a Kac-Moody symmetry, which is normally required to integrate non-Gaussian conformal field theories with continuous symmetry. We consider the sigma models on superspheres S$^{(2S+1|2S)}$ and projective superspaces CP$^{(N-1|N)}$. We proceed by studying a lattice regularization for these sigma models in term of fully packed intersecting loop models. Their transfer matrix algebra is a Brauer type algebra. The main strategy we employed in the research of exact results for these sigma models is the detailed study of the symmetries of the continuous theory, on one hand, and of the symmetries of the discretized model, on the other hand. This analysis provides a bridge between the behaviour of the discrete model and continuous theory. A detailed analysis of discrete symmetries - in particular the structure of the Brauer algebra blocks- combined with perturbative calculations gives rise to a proposal, as appropriate, to the partial or complete spectrum of the conformal field theory. An exact duality is also conjectured in the case of the sigma models on superspheres.