  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 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.
