Muslims are not allowed to change permanently or semi-permanently any of their physical appearence, and this include cosmetic plastic surgery. Allah says in surah An-Nisaa, verse 119, narrating the words of Iblis when he defied Allah: and indeed I will order them to change the nature created by Allâh.
However, Muslims are also encouraged to be healthy, and to seek medicinal help for their health problems. As such, plastic surgery for beautification per se is not allowed. But undergoing plastic surgery to restore a badly deformed body parts (due to accident or burn), is allowed since it will try to restore to the original state and it is something done out of necessity and not vanity.
Liposuction, which is removal of body fats by surgical methods, is allowed only for therapeutic purposes, such as when the fat is too much that it endangers one's life or endangers the pregnancy itself. But it should satisfy the following conditions:
* That there are no other safer and cheaper methods to lose weight.
* That the liposuction procedure itself has been agreed upon by credible doctors that it is safe, or has very high chance of success.