Comets impact the Earth very rarely, but these impacts can cause major environmental damage and greatly influence the course of evolution. Impacts with energies greater than 1 million megatons can loft sufficient dust into the atmosphere to cause a short-term cooling and lead to massive crop loss and starvation. If the energy is ten times larger, photosynthesis will cease for some weeks and the additional setting of fires from backfalling ejecta will lead to wildfires on a continental or even perhaps global scale. At an energy of 100 million megatons, there is environmental devastation on both land and sea and a substantial fraction of the life forms on Earth are in danger of extinction. If the impact energy is as high as 1 billion megatons, as it may be for comets as large as Hale-Bopp, very few terrestrial life-forms would survive the impact. With modern technology we can protect against impacts by short-period comets and asteroids, but long-period comets are much more difficult to detect, to predict, and to deflect. This paper discusses the possible effects of cometary impacts and the development of strategies for defending the planet. A Spaceguard Survey is the first step to detect and track NEOs (asteroids and short period comets). NASA has recently committed to the discovery and tracking of all NEOs larger than 1 km in diameter, working with the US Air Force and various international partners. However, the details of this Spaceguard Survey have not yet been established and are the subject of international discussions. In contrast, the appearance of a long-period comet on an Earth-impact trajectory presents a potential nightmare scenario, with little that can be done with modern technology to protect the planet. In summary: Now is the time to deal with the risk of asteroids and short-period comets, but protection against long-period comets is probably a task for later generations.