The magnetic and convective nature of the Sun's photosphere provides a unique platform from which generated waves can be modelled, observed and interpreted across a wide breadth of spatial and temporal scales. As oscillations are generated in-situ or emerge through the photospheric layers, the interplay between the rapidly evolving densities, temperatures and magnetic field strengths provides dynamic evolution of the embedded wave modes as they propagate into the tenuous solar chromosphere. A focused science team was assembled to discuss the current challenges faced in wave studies in the lower solar atmosphere, including those related to spectropolarimetry and radiative transfer in the optically thick regions. Following the Theo Murphy international scientific meeting held at Chicheley Hall during February 2020, the scientific team worked collaboratively to produce 15 independent publications for the current Special Issue, which are introduced here. Implications from the current research efforts are discussed in terms of upcoming next-generation observing and high-performance computing facilities. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.
Keywords: Sun: atmosphere; Sun: magnetic fields; Sun: oscillations; Sun: photosphere; sunspots; techniques: polarimetric.