Can sperm be grown in a lab dish ? Breakthrough Research suggests it may be possible. this may represent a future  solution for men with maturation arrest: article on Nature.

Sperm are very complex cells : they have a head a tail , need to be able to swim and penetrate an egg. Because of this male fertility can be affected by any disease of sperm envelopment. Often we hear about  immature sperm or morphologically abnormal sperm.

Researchers have been trying to grow sperm  In Vitro for a long time but without success.This work  was pioneered by Takehiko Ogawa and colleagues at Yokohama City University. The procedure involves taking biopsies of mouse testes, breaking them up into small  pieces, placing them on agarose gel  that has been partially soaked with a special medium, and letting them be for two months. If all goes according to plan, the chemicals in the medium would induce the gonadal stem cells to differentiate into mature sperm.

The secret of the success of this research has been to tweak the culture medium over time with different nutrients : it would be too complicated  to cover them here.
this is the kind of experiment that  is going to be very hard to reproduce by other labs as these guys have been at it for years and  , in this type of experiments, the secret is to follow a series of minute details.

Therefore clinical application of this technology  (for people) is years away. Another caveat is that in this technology is only valid if you have immature sperm to start with.  This is not a technique to make sperms from "scratch". Therefore men who have no immature sperm in their testicles would  not be helped with this method.  Nevertheless it is a huge leap!

Abstract below:

Spermatogenesis is one of the most complex and longest processes of sequential cell proliferation and differentiation in the body, taking more than a month from spermatogonial stem cells, through meiosis, to sperm formation^{1, 2}. The whole process, therefore, has never been reproduced in vitro in mammals^{3, 4, 5}, nor in any other species with a very few exceptions in some particular types of fish^{6, 7}. Here we show that neonatal mouse testes which contain only gonocytes or primitive spermatogonia as germ cells can produce spermatids and sperm in vitro with serum-free culture media. Spermatogenesis was maintained over 2 months in tissue fragments positioned at the gas–liquid interphase. The obtained spermatids and sperm resulted in healthy and reproductively competent offspring through microinsemination. In addition, neonatal testis tissues were cryopreserved and, after thawing, showed complete spermatogenesis in vitro. Our organ culture method could be applicable through further refinements to a variety of mammalian species, which will serve as a platform for future clinical application as well as mechanistic understanding of spermatogenesis. (source : Nature.com)

Link :  http://www.nature.com/nature/journal/v471/n7339/full/nature09850.html