3D printing technology has developed rapidly in the last decade. In addition to its common use in industrial field, 3D printing is gaining importance in medicine and pharmacy. This review provides information on the use of 3D printing in organ and tissue formation. It describes examples currently presented in this field of research, and the specific use of artificial tissues in clinical practice. The article also deals with the modelling of specific implants and prostheses tailored to the individual patient. Moreover, for complicated surgeries, 3D printing is used to create models which are used to practise and select the correct surgical procedure. The use of 3D printers in the production of medicines and specific drug delivery systems is also discussed. Due to the development of 3D bioprinting in tissue engineering, the second part of the article is devoted to a detailed overview of biocompatible materials and bioinks, accompanied by specific examples of their use.