During the past 10 years the world has experienced enormous progress in the organoids field. Human organoids have shown huge potential to study organ development, homeostasis and to model diseases in vitro. The organoid technology has been widely and increasingly applied to generate patient-specific in vitro 3D cultures, starting from both primary and reprogrammed stem/progenitor cells. This has consequently fostered the development of innovative disease models and new regenerative therapies. Human primary, or adult stem/progenitor cell-derived, organoids can be derived from both healthy and pathological primary tissue samples spanning from fetal to adult age. The resulting 3D culture can be maintained for several months and even years, while retaining and resembling its original tissue’s properties. As the potential of this technology expands, new approaches are emerging to further improve organoid applications in biology and medicine. This review discusses the main organs and tissues which, as of today, have been modelled in vitro using primary organoid culture systems. Moreover, we also discuss the advantages, limitations, and future perspectives of primary human organoids in the fields of developmental biology, disease modelling, drug testing and regenerative medicine.