Now there is a new phenomenon that is setting physical and chemical effects in motion. Humans are adding CO2 to the atmosphere at a rate of over 26 billion tons per year, turning the earth's natural "greenhouse effect" into a "car in the hot sun" effect. The basics of the chemical mechanism for this is not hard to understand. Carbon dioxide does not absorb energy at the wavelengths of visible light, so it is largely transparent to light arriving from the sun. Sunlight, however, gets absorbed by the ground and is re-radiated up into the atmosphere as long-wave infrared radiation, or heat. It happens that carbon dioxide absorbs infrared radiation quite readily, then re-radiates it in all directions, heating the atmosphere. We have satellite data going back to 1970 that actually shows the decrease in long-wave infrared radiation escaping into space because it has increasingly been trapped in the lower atmosphere.
So you asked to what extent we can control global warming. It is in a way very fortunate that we are the cause of this warming, because it means that we can indeed control it by moving away from a fossil fuel economy. The cost of solar is plummeting and the use of batteries for local storage is moving into the mainstream. In fact, Barclays has downgraded the entire US electrical utility sector because they believe that the combination of solar and local storage will soon be disruptive (From Business Insider: Barclays Has The Best Explanation Yet Of How Solar Will Destroy America's Electric Utilities.) Bill Gates argues we need R&D on a Manhattan Project scale to pursue an array of strategies, including safe nuclear options, such as traveling wave reactors, which use spent fuel. As he points out, one molecule of uranium has a million times the energy of a molecule of coal.
As Bill Gates puts it, to meet the requirement of getting to a zero carbon economy by 2050, "we have 20 years to invent and then 20 years to deploy" (Transcript of "Innovating to zero!".) Getting there is a tall order, but within reach if we take action now. We won World War II, we can win this.