In the lead-up to the Square Kilometre Array (SKA) project, several next-generation radio telescopes and upgrades are already being built around the world. These include APERTIF (The Netherlands), ASKAP (Australia), e-MERLIN (UK), VLA (USA), e-EVN (based in Europe), LOFAR (The Netherlands), MeerKAT (South Africa), and the Murchison Widefield Array. Each of these new instruments has different strengths, and coordination of surveys between them can help maximise the science from each of them. A radio continuum survey is being planned on each of them with the primary science objective of understanding the formation and evolution of galaxies over cosmic time, and the cosmological parameters and large-scale structures which drive it. In pursuit of this objective, the different teams are developing a variety of new techniques, and refining existing ones. To achieve these exciting scientific goals, many technical challenges must be addressed by the survey instruments. Given the limited resources of the global radio-astronomical community, it is essential that we pool our skills and knowledge. We do not have sufficient resources to enjoy the luxury of re-inventing wheels. We face significant challenges in calibration, imaging, source extraction and measurement, classification and cross-identification, redshift determination, stacking, and data-intensive research. As these instruments extend the observational parameters, we will face further unexpected challenges in calibration, imaging, and interpretation. If we are to realise the full scientific potential of these expensive instruments, it is essential that we devote enough resources and careful study to understanding the instrumental effects and how they will affect the data. We have established an SKA Radio Continuum Survey working group, whose prime role is to maximise science from these instruments by ensuring we share resources and expertise across the projects. Here we describe these projects, their science goals, and the technical challenges which are being addressed to maximise the science return.