Scientists from Yakohama City University managed to grow human liver in mice. Of course, this liver is not human-sized, but its structure and functions are the same to human liver.
The liver was cultivated from three types of human cells. First, iPSC from human skin were made. The genes responsible for growth and proliferation of liver cells were activated. Second, the endothelial cells from grow umbilical cord serum were added to generate blood vessels. The third component of the mixture was mesenchimal cells, which are origins of bones and fat.
Once Takanori Takebe observed that cells, cultivated together, organazing into 3D structures. After that a lot of attemts were made to achive ideal prorortion of cells.
Little livers grew up to 4 mm in diameter, after that they were injected into mouse, where liver starts to secrete proteins. Moreover, this cell transplants formed their own vessels and connected to mouse's vessels system.
Thus, the main problem of organ' sgrowing seems to be solved.