Coarse Liver tissue can be printed so far. Food such as pizza may be printed out soon. I am wondering how far these technique can work on transplant of severed limb or small such as cut fingers.
Printed pizza? So that means a Star Trek food synthesizer will become reality one day. Yum.
Research is already happening on protein scaffolds for body parts. Maybe we can use 3D printing for that. I guess the principle of operation might have to be modified so that the 3D printer does it without cooking your protein.
They have been working toward 3D printed organs and prosthetics for a few years now. As I understand it, one of the main challenges is the ability to make the incredibly delicate capillary networks required for micro-perfusion of the printed tissues. They tried to work with VEGF (Vascular Endothelial Growth Factor), but it didn't work nearly as well as they had hoped.
Here are some papers I found that might answer your question in more detail.