Folkstyle
The main style of wrestling practiced in the US is called Folkstyle (collegiate) wrestling which is a very similar to Freestyle in that you can use all holds more or less, including grabbing and using the legs to throw, takedown, ride and hold the opponent.
The main difference between Folkstyle and Freestyle is that Folkstyle encourages wrestlers to escape holds and do reversals by rewarding points for them where as Freestyle and Greco do not reward points for this. Another interesting difference is in Folkstyle you cannot lock your hands while riding an opponent in par terre unlike in Freestyle and Greco, you can lock your hands at any time. This specific rule leads to many more escaped and reversals on rides and a lot of techniques that you will not see in other styles of wrestles as the absence of the clasping hands on rides leaves much room to escape and reverse for points.
Folkstyle is engrained in the US collegiate system and is a really exciting style to watch for reversals and escapes.