It's already been done in Sweden. Now the first uterus transplants are going to be performed in the US, on a study group of women who are infertile because of uterine deformity (or absence).
The women will be able to get pregnant only through IVF, as its currently too complicated to hook up the donor womb to the woman's fallopian tubes. And they'll have to give birth via c-section.
What about trans women?
The team say it's possible, but only for trans women who have had bottom surgery and some pelvic reconstruction to allow space for the pregnancy to develop, and it would require a lot of hormones. Right now, they're not taking applicants - but it does hint at the possibility that a trans woman could carry a child...even her own (many trans women are now freezing sperm samples before having surgery).