The comparison of macromolecular structures, in terms of functionalities, is a crucial step when aiming to identify potential docking sites. Drug designers require the identification of such docking sites for the binding of two proteins, in order to form a stable complex. This paper presents a review of current approaches to macromolecular structure comparison and docking, following an algorithmic approach. We describe techniques based on the Bayesian framework, kernel-based methods, projection-based techniques and spectral approaches. We introduce the use of quantum particle swarm optimization, in order to aid us to find the most appropriate docking sites. We discuss the importance of the heat and Schrodinger equations to address the non-rigid nature of proteins and highlight the strengths and limitations of the various methods.