Galaxies emit radiation through a number of different mechanisms in the range 1 GHz to 1 THz, including synchrotron radiation, free-free emission, and thermal dust emission. In addition, 'anomalous microwave emission' (AME) has been detected in our Galaxy at frequencies of 10-100 GHz, and is thought to be due to spinning dust grains. Each of these components is present in different amounts, and with different spectral parameters, depending on the physical environments of each galaxy - and it is an open question about where AME is located, and whether it is a property of only special parts of some galaxies or if it is present everywhere in all galaxies. In this talk, I will summarize my recent work in understanding the spectra of the large-scale emission from our Galaxy and that from other nearby galaxies. In particular, I will focus on the question of whether AME in our Galaxy could be flat-spectrum synchrotron radiation rather than spinning dust (arXiv:1112.0432); searching for new regions of AME in our Galaxy using Planck data (arXiv:1101.2031); and whether AME is present in the integrated spectrum of nearby galaxies (arXiv:1105.6336).