Let \(R\) be a ring with identity, all \(R\)-modules in the paper are considered to be left modules and unitary. Using proper resolutions of modules over \(R\), the authors of this paper discuss relative homological dimensions and relative derived functors. More specifically if \(\mathcal{X}\) is a class of \(R\)-modules and \(F\) is a functor, they associate a right derived functor \(R^n_{\mathcal{X}}F(-)\) to every \(R\)-module with a proper right \(\mathcal{X}\)-resolution. They also define left derived functors \(L_n^{\mathcal{X}}F(-)\) in a similar way. Then, the authors study the relationship between \(R^n_{\mathcal{X}}F(-)\) and \(R^n_{\mathcal{X}^\prime}F(-)\) for two classes of \(R\)-modules \(\mathcal{X},\mathcal{X}^\prime\). They prove that under some technical assumptions these two derived functors agree. Inspired by the classical definitions of projective, injective and flat dimension of an \(R\)-module, the authors give a definition of \(\mathcal{X}\)-dimension of an \(R\)-module and study the properties of this dimension. Using this \(\mathcal{X}\)-dimension, they define a global dimension for \(R\) and study its properties. They then show how the comparison of relative cohomology theories is related to generalized Tate cohomology theories. The authors end the paper by showing the existence of derived functors with respect to the Auslander and Bass classes of \(R\)-modules and give some applications.