Perturbations in CFTs

I will discuss the aspects of the perturbations in CFTs from two different points of view. The first point of view is rephrasing the usual perturbation in QFT in the modern language of Conformal Bootstrap. More specifically I will discuss the epsilon-expansion in phi^4 theory from the bootstrap point of view. The second point of view is to try to form a statement about the deformation of a strongly coupled CFT by a marginal operator.