Thesis (Ph.D.) - Indiana University, Department of Physics/University Graduate School, 2019Confinement and chiral phase transitions are remarkable non-perturbative phenomena emerging from Quantum Chromodynamics, that is, the underlying theory of the strong interaction between subatomic particles. A theoretical understanding of these transitions and their interrelations is of fundamental importance. While it is widely perceived that their dynamics arises from nontrivial topological configurations in Yang-Mills theories, a concrete and sophisticated realization of such idea is an outstanding challenge. In this work, significant progress is presented along this direction by the construction of a new framework based on a statistical ensemble of topological objects called instanton-dyons, namely, the constituents of the finite-temperature instantons with non-trivial holonomy. I present a comprehensive numerical study of the confining properties in SU(2) Yang-Mills theory at finite temperature, obtaining important observables which are then compared with available data from state of the art simulations of lattice gauge theory and are found to be in substantial agreement. Furthermore, with the inclusion of dynamical quarks in the system, I explore the non-trivial interplay between the confinement/deconfinement and chiral symmetry breaking/restoration phase transitions.