Star formation and nuclear activity in luminous infrared galaxies: an infrared through radio review

Nearby galaxies offer unique laboratories allowing multi-wavelength spatially resolved studies of the interstellar medium, star formation and nuclear activity across a broad range of physical conditions. In particular, detailed studies of individual local luminous infrared galaxies (LIRGs) are crucial for gaining a better understanding of these processes and for developing and testing models that are used to explain statistical studies of large populations of such galaxies at high redshift for which it is currently impossible to reach a sufficient physical resolution. Here, we provide an overview of the impact of spatially resolved infrared, sub-millimetre and radio observations in the study of the interstellar medium, star formation and active galactic nuclei as well as their interplay in local LIRGs. We also present an overview of the modelling of their spectral energy distributions using state-of-the-art radiative transfer codes. These contribute necessary and powerful `workhorse' tools for the study of LIRGs (and their more luminous counterparts) at higher redshifts which are unresolved in observations. We describe how spatially-resolved time-domain observations have recently opened a new window to study the nuclear activity in LIRGs. We describe in detail the observational characteristics of Arp 299 which is one of the best studied local LIRGs and exemplifies the power of the combination of time-domain and high-resolution observations at infrared to radio wavelengths together with radiative transfer modelling used to explain the spectral energy distributions of its different components. We summarise the previous achievements obtained using high-spatial resolution observations and provide an outlook into what we can expect to achieve with future facilities.