It's the goal of the Paris Agreement to limit global warming to 1.5°C above pre-industrial levels. The 2018 IPCC report says that the world has a budget of about 420 GtCO2, to have a 66% chance to stay within that 1.5°C. By dragging the knob you can see that if we would cut down right now, we would have to get to zero emissions around 2040. (The IPCC itself uses a 50% chance, which means zero emissions at 2050.)
That said, 1.5 degree warming is still pretty bad. It's hard to model the exact consequences on us, but we know some things. By the end of the century:
After 1.5°C warming, 2.0°C is the next big threshold. We want to stay well under this per the Paris Agreement. The budget is about 1170 GtCO2 since 2018 (which includes the 1.5°C budget).
It is harder to predict what would happen in this case, since it's further out, but to give you an idea, by the end of the century:
When we get past 2.0°C, things get tricky. Self-reinforcing natural feedback loops get activated, which can accelerate warming automatically, to potentially above 10.0°C. This would cause mass extinction of species, and make much of the planet uninhabitable. See these resources for more information.