Canada has thriving communities in CMB (cosmic microwave background) studies, cosmology and submillimetre (submm) astronomy, with involvement in many facilities that featured prominently in previous Astronomy Long Range Plans. The standard cosmological model continues to be well fit using a small number of parameters. No one expects this model to be complete and so we need to continue to challenge it with data; moreover, it does not explain how galaxies and other structures form. So, how do we improve the precision of our understanding of structure formation within this model? Wavelengths from the microwave to the submm will be particularly fruitful for answering this question. That's because, in addition to the CMB anisotropies, there are other signals that can be extracted from large maps at these wavelengths - particularly the cosmic infrared and submm backgrounds, the thermal and kinetic Sunyaev-Zeldovich effects, and CMB lensing. Such signals carry a wealth of information about the cosmological model, as well as how dust, gas and star-formation evolve within dark-matter halos. Cross-correlations between these signals and those coming from the radio, optical and X-ray surveys, will provide even more information. Canadians are already members of teams for several related facilities and are working to be involved in others. In order for Canada to be fully engaged in exploiting the detailed information coming from these cosmological signatures, it is crucial that we find the resources to participate competitively in a combination of projects currently being planned. Examples include CMB-S4, CCAT-prime, AtLAST, a new camera for JCMT, balloon projects such as BFORE and a future ambitious CMB satellite.