Globins are a family of proteins characterized by the presence of the heme prosthetic group and involved in variety of biological functions in the cell. Due to their biological relevance and widespread distribution in all kingdoms of life, intense research efforts have been devoted to disclosing the relationships between structural features, protein dynamics, and function. Particular attention has been paid to the impact of differences in amino acid sequence on the topological features of docking sites and cavities and to the influence of conformational flexibility in facilitating the migration of small ligands through these cavities. Often, tunnels are carved in the interior of globins, and ligand exchange is regulated by gating residues. Understanding the subtle intricacies that relate the differences in sequence with the structural and dynamical features of globins with the ultimate aim of rationalizing the thermodynamics and kinetics of ligand binding continues to be a major challenge in the field. Due to the evolution of computational techniques, significant advances into our understanding of these questions have been made. In this review we focus our attention on the analysis of the ligand migration pathways as well as the function of the structural cavities and tunnels in a series of representative globins, emphasizing the synergy between experimental and theoretical approaches to gain a comprehensive knowledge into the molecular mechanisms of this diverse family of proteins.