Modal logics are logical systems that enable us to examine of possibilities and necessities in different senses when modeling certain problems. In recent years, the application of this field has gained an increasingly important role in computer science, theoretical linguistics, or mathematical logic. The focus of my research is the model-theoretic investigation of modal logics and systems related to them, with particular attention paid to the model-theoretic and algebraic features of the so called ultrafilter extensions construction, and its  algebraic  counterpart. The theoretical study of these constructions has now become an essential area in the understanding of Boolean algebras with operators and their associated logical systems, as well as their applicability.