The historic Paris Agreement calls for limiting global temperature rise to “well below 2 °C.” Because of uncertainties in emission scenarios, climate, and carbon cycle feedback, we interpret the Paris Agreement in terms of three climate risk categories and bring in considerations of low-probability (5%) high-impact (LPHI) warming in addition to the central (∼50% probability) value. The current risk category of dangerous warming is extended to more categories, which are defined by us here as follows: >1.5 °C as dangerous; >3 °C as catastrophic; and >5 °C as unknown, implying beyond catastrophic, including existential threats. With unchecked emissions, the central warming can reach the dangerous level within three decades, with the LPHI warming becoming catastrophic by 2050. We outline a three-lever strategy to limit the central warming below the dangerous level and the LPHI below the catastrophic level, both in the near term (<2050) and in the long term (2100): the carbon neutral (CN) lever to achieve zero net emissions of CO2, the super pollutant (SP) lever to mitigate short-lived climate pollutants, and the carbon extraction and sequestration (CES) lever to thin the atmospheric CO2 blanket. Pulling on both CN and SP levers and bending the emissions curve by 2020 can keep the central warming below dangerous levels. To limit the LPHI warming below dangerous levels, the CES lever must be pulled as well to extract as much as 1 trillion tons of CO2 before 2100 to both limit the preindustrial to 2100 cumulative net CO2 emissions to 2.2 trillion tons and bend the warming curve to a cooling trend.