Polygyny is legal.  Legal status unknown or ambiguous.  Polygyny generally illegal, but its practice not fully criminalized.  Polygamy outlawed or abolished and its practice criminalized.

Men and women can have as many spouses as they can fit into a lifetime; but this is not generally approved. Women are requested to have only one husband at a time (there is evidence that wealthy Arab women were polyandrous before the coming of Islam - certainly wealthy men were polygynous), and men are limited to four at one time, whereas previously there had been no limit, and a wealthy and generous man was expected to cater for as many women as he could afford (in the absence of a welfare state). ...  No Muslim was ever to deliberately cause hurt or harm to another Muslim, so a man might not take extra womenfolk into his home if it would cause upset and distress (it was recommended when there were lots of widows after warfare, if the women were willing to be generous to bereft 'sisters'). Also, if a man could not provide equal treatment of his wives - equal food, clothing, money, living quarters, time spent with - he was refused permission for polygamy. Equal sexual activity was not ruled on, however. Some wives had no sexual relationship with their husbands at all after a while, or if they came into the household as widows of relatives." / ©BBC "BBC - Religions - Islam: Sharia."