Continuous manufacturing of biologics (biopharmaceuticals) has been an area of active research and development for many reasons, ranging from the demand for operational streamlining to the requirement of achieving obvious economic benefits. At the same time, biopharma strives to develop systems and concepts that can operate at similar scales for clinical and commercial production—using flexible infrastructures, such as single-use flow paths and small surge vessels. These developments should simplify technology transfer, reduce footprint and capital investment, and will allow to react readily to changing market pressures while maintaining quality attributes. Despite a number of clearly identified benefits compared to traditional batch processes, continuous bioprocessing is still not widely adopted for commercial manufacturing. This paper details how industry-specific technological, organizational, economic, and regulatory barriers that exist in biopharmaceutical manufacturing are hindering the adoption of continuous production processes. Based on this understanding, the roles of process systems engineering (PSE), process analytical technologies, and process modeling and simulation are highlighted as key enabling tools in overcoming these multi-faceted barriers in today’s manufacturing environment. Of course, we do recognize that there is also a need for a clear set of regulations to guide a transition of biologics manufacturing towards continuous processing. Furthermore, the role played by the emerging fields of process integration and automation as well as digitalization is explored, as these are the tools of the future to facilitate this transition from batch to continuous production. Finally, an outlook focusing on technology, management, and regulatory aspects is presented to identify key concerted efforts required to drive the broad adaptation of continuous manufacturing in biopharmaceutical processes.