Standard Model determinations of properties of strongly interacting systems of hadrons have become possible with the powerful method of lattice quantum chromodynamics (LQCD), a method with growing applicability and reliability. While growth in computational power and innovations in algorithmic and computational approaches have been essential in advancing the state of the field, conceptual and formal developments have played a crucial role in turning the output of LQCD computations to phenomenologically valuable results. From the invention of finite-volume technology to access physical observables by Martin Luescher over three decades ago to date, this field has grown in scope and complexity, enabling studies of scattering amplitudes and reaction rates, as well as spectroscopy of excited states of quantum chromodynamics (QCD) and resonances. Further, LQCD studies are augmented with the inclusion of quantum electrodynamics (QED), and subtleties related to the finite volume of systems in presence of QED have been understood and largely controlled. In this talk, I focus on selected developments to give a taste of the status of the field concerning the mapping between the finite and infinite-volume physics and its state-of-the-art applications.