In this thesis we use various methods to study the interaction of hadrons. We focus on topics related to exotic hadrons, such as tetraquarks from meson-meson interaction, pentaquarks from meson-baryon, and also triangular singularities. We show how experimental data can be explained with our theoretical models, and make predictions that can be compared with future experiments. In chapter 1 we show our method to describe meson-meson interactions, known as chiral unitary approach, showing how the interaction of pseudoscalars generates the f0(500), f0(980) and a0(980), which appear in the two articles discussed in this chapter: that of the eta_c -> eta pi+ pi- decay, and that of the a0(980)-f0(980) mixing in chi_c1 -> pi0 pi0 eta and chi_c1 -> pi0 pi+ pi-. Both works share common features of a method used in an earlier study of the chi_c1 -> eta pi+ pi- decay, which consists in using SU(3) symmetry to see the weight of different trios of pseudoscalars produced in the charmonium decay c cbar -> 123. In chapter 2 we show a method for studying meson-baryon interactions and looking for new states as poles in the scattering amplitude. We discuss how to extend the local hidden gauge approach to the charm sector, through the exchange of light vectors with SU(3) symmetry and the heavy quark as spectator. We present three papers: the one on the five Omega_c states recently discovered by the LHCb collaboration, three of them in remarkable agreement with our calculations; then the follow-up article on how to observe these states in the weak decay Omega_b -> Xi_c+ K- pi- and a third one with predictions for Omega_b molecular states. In chapter 3 we see how triangular singularities can be formed in the decay A -> 1+R, followed by R -> 2+3 and the rescattering 1+2 -> 1'+2'. We see that in the case when there is a resonance from the rescattering, at the same energy corresponding to the singularity, its effect can be seen in the experiment and misinterpreted as a new state. In our first work we study the production and decay of the f1(1285) in pi a0(980) and K* Kbar. We find an enhancement tied to a triangular singularity concluding that the f1(1420) is not a genuine resonance, but the manifestation of these decay modes at higher energies. Next, we study the reaction gamma p -> p pi0 eta paying attention to the two main mechanisms at low energies, gamma p -> Delta(1700) -> eta Delta(1232) or pi N(1535), where the second involves a triangular singularity. Finally, we investigate the Schmid theorem that states the possible triangle singularity developed by the elastic reescattering does not change the cross section provided by the tree level. We investigate the process in terms of the width of the unstable particle produced and determine the violation and the limits for validity of the theorem. Overall we have shown the importance of the dynamically generated states and how this description should be part of our understanding of the fundamental properties of matter.