There are a lot styles of wrestling in the world. In the U.S., many styles are practiced daily. I will tell you about four of the main styles.
First of all, there is the Greco-Roman style. Greco-Roman, probably the oldest style, is very popular. In this style, competitors must apply all holds above the waist and are not allowed to use their legs to defend themselves or attack. The objective is to throw your opponent to the mat.
Greco-Roman is very close to Freestyle wrestling. The only difference is that competitors are allowed to use their legs to defend and score. Freestyle focuses on attacking all of the body. Points are scored when your opponent's back is exposed on the mat.
The next style is Folkstyle. Folkstyle wrestling is commonly seen in high school or college competitions in the United States. Folkstyle focuses on control. Points are given if a person controls their opponent longer than their opponent controls them. Folkstyle, like Freestyle, has wrestlers starting out on their feet and then going down to the mat to gain control. This style is also known as collegiate or scholastic styles.
Judo is a wrestling style started in Japan. Judo means soft sport. The objective is to throw your opponent off of their feet and get them into a submission hold. After one wrestler is taken down, time continues to run for a short amount of time to see if one of the wrestlers can achieve a submission or a pin. Judo, along with Greco-Roman and Freestyle are all recognized as Olympic sports.
The final style, Sombo, was started in Russia. Sombo combines Greco-Roman, Freestyle, and Judo. Sombo allows wrestlers to throw and submit opponents, but no pins are allowed and back points can be scored only once. Choke holds are also not allowed in Sombo.