The competition of antiferromagnetic and d-wave superconductivity order parameters in cuprates is studied within a phenomenological model. An unbiased numerical analysis is carried out. The results suggest that the transition from the antiferromagnetic to the superconducting region is not universal. When disorder is present, a glassy state forms leading to the possibility of "colossal" effects in some cuprates, analog of those in other transition metal oxides, in particular manganites. Non-superconducting Cu-oxides could rapidly become superconducting by the influence of weak perturbations. Consequences of this mechanism for thin-film and angle-resolved photoemission experiments are discussed. In addition, a recent study of the strong-coupling region in d-wave superconductors with a numerically exact technique is briefly reviewed.