While packed bed chromatography, known as conventional chromatography, has been serving the biopharmaceutical industry for decades as the bioseparation method of choice, alternative approaches are likely to take an increasing leading role in the next few years. The high number of new biological drugs under development, and the need to make biopharmaceuticals widely accessible, has been driving the academia and industry in the quest of anything but conventional chromatography approaches. In this perspective paper, these alternative approaches are discussed in view of current and future challenges in the downstream processing field.