The Additive manufacturing 3D printing is a process of creating a three dimensional solid objects or rapid prototyping of 3D models from a digital file, which builds layer by layer. The 3D bioprinting is a form sophisticated of 3D printing technology involving cells and tissues for the production of tissue for regenerative medicine, which is also built layer by layer into the area of human tissue or organ. This paper defines the modern methods and materials of the AM, which are used for the development of physical models and individually adjusted implants for 3D printing for medical purposes. The main classification of 3D printing and 3D bioprinting technologies are also defined by typical materials and a field of application. It is proven that 3D printing and 3D bioprinting techniques have a huge potential and a possibility to revolutionize the field of medicine.