Conformal manifolds are families of conformal field theories connected by exactly marginal deformations. They are ubiquitous in theories with supersymmetry, while there are no examples, at least in d>2, in non-supersymmetric setups. One can question whether they can ever exists. In this talk I address these issues by looking at the constraints that a conformal field theory should enjoy to admit exactly marginal deformations. In particular, I derive a sum rule the CFT should satisfy, and discuss some of the implications that this has on the CFT spectrum and OPE coefficients. Then, I will focus on conformal field theories admitting a gravity dual description, and as such a large-N expansion. I will discuss the relation between conformal perturbation theory and loop expansion in the bulk, and show how such connection could help in the search for (non-supersymmetric) conformal manifolds beyond the planar limit. Using a toy-example, I will show that this is not an empty set.