In this thesis we study the formalization of abduction in modal frames. Over the last decade researchers focus on modal frames. The typical modal operators can formalize the diversity between knowledge and beliefs. Also, we can construct some many-world models of ascending cardinality. Our main issues are the criteria of selecting the best explanation and their possible correlation. In introduction we sketch some abductive inferences and show some applications in science and philosophy. The second chapter contains a vast presentation of selective abductions due to Schurz and a brief presentation of some explanatory virtues. The third chapter contains the many-world approach of Soler-Toscano, Fernandez-Duqueand Nepomuceno-Fernandez. In the fourth chapter we present the dynamic proofs approach, as defined by Gauderis. Chapter 5 and 6 consist in a brief discussion of these models. We examine if they formalize every possible selective abduction and if they satisfy any of the explanatory virtues. Chapter 7 contains an alternative approach for formalizing consilience. The final chapter contains the conclusion and some open problems.