Star forming galaxies (SFGs) are powerful factories of high-energy cosmic rays. Their star formation rate (SFR) is a key physical property characterizing both the total energy budget and the transport conditions of such particles populations. Tight correlations are in fact observed between the SFR and the non-thermal radio and gamma-ray luminosity of several SFGs. I will discuss the nature of such correlations focusing on the physical implications on the particle transport. The most active SFGs are known as starburst galaxies (SBGs). These objects are unique environments for cosmic rays since they might be able to confine most of their injected particles. Such a calorimetric scenario is of great interest for the production of hadronic byproducts such as non-thermal radiation and high-energy neutrinos. I will illustrate the main features and the impact of calorimetry on the spectral energy distribution of these galaxies. In addition, since SBGs are also inferred to be highly numerous at cosmological distances, I will discuss their possible contribution to the diffuse fluxes of gamma rays and neutrinos observed by Fermi-LAT and IceCube respectively.
Despite of the extreme conditions expected to be found in the interstellar medium of SBGs, accelerators of sub-galactic scale such as supernova remnants or star clusters are unlikely to overcome the PeV range. On the other hand, the enhanced rate of supernovae characterizing SBGs can launch powerful winds with bubble structures where particles can be efficiently accelerated at higher energies. I will discuss a physical model describing particle acceleration and transport in these galactic wind bubbles. Finally, I will conclude presenting the multi-messenger potential of SBGs in terms of gamma rays, neutrinos and escaping cosmic rays.