This is the question(Is polygamy illegal?) that many people might have in mind and the answer is going to be very simple:
It all comes to the country where you are located. This means that the legal status of the polygamy is going to be different from one country to another. This way what might be illegal in one country might be perfectly normal in another.
Right now you can find many countries out there where polygamy is not permitted and in case a person is going to get married while being still married to another person is going to automatically commit the crime of bigamy which is most of the time persecuted by the authorities and in almost all the cases the second marriage is going to be automatically considered to be null and void. This way even with the consent of the first spouse you still cannot get the second marriage to be valid.
This way in the countries where the is polygamy illegal there are a certain number of people that are practicing "serial monogamy". Here a person is going to marry and divorce multiple partners.
Right now almost all the western civilization and countries are strictly prohibiting the polygamy, but there are still a few of them that recognize the polygamous marriages.
In most European countries for example the polygamy is considered to be a crime and it can be punished with prison time. Therefore the moment a person is going to try to get married with more than one partner is most likely going to get into a lot of trouble.
In United States the polygamy represents an illegal practice in all 50 states. However almost one century ago in the year 1900 there were many people practicing polygamy in and around the Utah state, but the United States federal government has forced them to abandon this practice. But the truth is that the American Muslims which represent a small minority of around 50k-100k people that are living in illegal polygamous relationships.
In Canada the polygamy is illegal thanks to the Section 293 of the Criminal Code of Canada and the bigamy is banned at Section 290. But at the same time it's been more than 60 years since the last person was prosecuted for practicing it.
In other countries like the ones that you can find in Africa, Asia (this includes India) you can still find polygamy to be accepted by both the law and the society.
The best way to answer your question whether polygamy is illegal or not is going be given to you based on the country where you are living.