Open Skies allows airlines from one country to start a route to a country that also participates in Open Skies and to charge whatever price the market will bear.
The first Open Skies routes from the US were to central Europe... all of the EU has Open Skies with the US and slots are available to most airports in the EU except for to/from LHR.
The US and S. Korea, Taiwan, Singapore and others have Open Skies in Asia.
The biggest countries of Latin America including Brazil and Colombia do not have Open Skies with the US but that will change within the next couple years. Some countries allow new routes to/from certain cities, but not others. São Paulo-GRU has limited terminal facilities but will be adding them in the next couple years but for now US airlines cannot add more flights to GRU. US wants to start service there but cannot... DL will likely add more GRU service. GRU is the largest market in S. America.
Part of why AA does so well in Latin America is because there are limitations that prevent other US carriers from starting the most valuable routes including to-from MIA on one end or the largest markets in Latin America on the other end. Any one of the US airlines is far larger and more powerful than their peers in Latin America... combined they have the potential to wipe out the Latin airlines and thus the fear of Open Skies.
But the US also does not allow anti-trust immunity or joint ventures with airlines in countries where there is not Open Skies.