The SM of particle physics is the simplest theory that can successfully describe the fundamental components of matter and their interactions. Nevertheless, it cannot be the ultimate theory as there are certain theoretical aspects and experimental evidence that he is unable to explain. This fact is what motivates the present thesis in which NP models that are able to give explanation to some of these problems have been explored. Part I introduces the theoretical bases that support the thesis. In the chapter 1 the SM is described with a certain level of detail, the elementary particles and their interactions are presented. In addition, a review of the theoretical problems and experimental evidence that give rise to the study of physics beyond SM is made. The second chapter presents a minimal extension of the SM, known as 2HDM in which the scalar sector is extended with a second Higgs doublet. Part II focuses on the theoretical aspects of the research carried out during the doctoral period. In particular, we focus on studying the scalar extensions of the SM that do not generate significant contributions to processes SFCNC. These processes are heavily suppressed both in the SM and experimentally and any extension of the SM must suppress them to be compatible with the observations. The condition that there are no tree-level SFCNC (first-order on perturbation theory) implies that Yukawa matrices can be diagonalized simultaneously. Models that meet this have been extensively studied in the literature and are known as models with NFC. For example, the aligned 2HDM model requires that Yukawa matrices be proportional to each other at a given energy scale but, in general, this condition is not satisfied at other scales due to quantum corrections, as studied in chapter 3. In chapter 4, a generalization of the models known as BGL is developed. While BGL models satisfy the MFV conditions, gBGL do not but the generated SFCNC in the up and down quark sectors are controlled by elements of the CKM matrix. Generated by the same symmetry that gives rise to the generalized BGL models of the previous chapter, in chapter 5 a model that offers a connection between the phases of the CKM and PMNS mixing matrices is presented. Inspired by the parameterization of the Yukawa matrices of gBGL models, in the chapter 6 a systematic study of the different models generated from abelian symmetries that can be parameterized of analogous way to the BGL models and gBGL is made. Part III focuses on the phenomenological aspects addressed in this thesis. In chapter 7 it is possible to find all the experimental results used in the following chapters when adjusting the parameter space of the models presented in Part III. Chapter 8 provides a general analysis of the parameter space of gFC models. Finally, in chapter 9 two particular cases of the model known as gFC where the anomalies of the magnetic moment of the electron and the muon are explained simultaneously are studied.