The biological industry, but also biorefining platforms in the context of the circular economy, have been fertile terrains for the development of a palette of novel products of increasing structural diversity and fields of application. To mention only a few of the more complex bioproducts, we can consider monoclonal antibodies, plasmid DNA, virus‐like particles and exosomes. Of course, some products of industrial relevance are much simpler in nature. Irrespective of the product class and field of application, a shift from batch processing to continuous manufacturing is currently happening. This is due to the fact that operating in the continuous mode can result in process intensification, and therefore increased productivity with lower environmental impact can be realized. Some biological production schemes, e.g. those based on perfusion cultures, are well known in the pharmaceutical industry. Likewise, continuous fermentation is now utilized to produce ethanol from biomass. In many cases, continuous downstream operations are desired but difficult to implement; there is a pressing need to better understand the available options for product recovery and purification. Some traditional methods require re‐evaluation in modern contexts and some others, of experimental nature, require further improvement before actual implementation. In this article, we present an overview of the most promising methods that would allow for robust downstream bioprocessing options in the near future – with a focus on adsorption technologies. © 2021 The Authors. Journal of Chemical Technology and Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry (SCI).