While asteroid impacts of consequence are rare, at their most devastating they are existential threats. The most recent one occurred 66 million years ago resulting in the demise of the dinosaurs and approximately 75% of all species living at the time. While extremely infrequent (approximately once per 100 million years), the earth has likely experienced more than 45 impacts of this size or larger since its formation.
The consequences of much smaller and more frequent impacts are still of great concern to life on Earth. Civilization-destroying impacts likely occur every few hundred thousand years. So-called "city killers" occur on the order of once per 3-400 years or so.
Technology exists today that enables us, with adequate early warning, to prevent these smaller impacts. A deflection, i.e. slightly altering the asteroid's orbit such that it just misses the earth, while simple in principle, has many subtle details embedded within it.
The early warning necessary to execute a deflection is also simple in concept while involving many detailed subtleties. Telescopic observations, occasionally supplemented by radar observations, are used to discover Earth-approaching asteroids (referred to as NEOs - near-Earth objects), determine their orbits, and predict future impacts.
The technologies for both early warning and deflection are evolving rapidly regarding both capability and cost. For smaller NEOs the cost of a deflection campaign may dramatically exceed the cost of evacuating a local impact zone, and the decision will be based on sociopolitical factors, not technical ones.
Aside from the deflection/evacuation decision above, perhaps the source responsible for the most challenging geopolitical decisions is inherent in the deflection process per se. While the physical act of deflection takes place entirely in space, the consequences of this process occur on Earth. In effect, the deflection process shifts the original impact point across the surface of the planet until it misses the planet altogether. This path across the planet, however, is not arbitrary. It is a narrow corridor, often 100 km or less wide, that extends across the entire width of the planet. The original impact point can, hypothetically, only be dragged along this corridor in one direction or its opposite, until off the earth. However, in most instances, there are several nations and many people not originally threatened by the impact that will, should something go wrong during the deflection, be put at risk as the impact point passes by them. In effect, people (think cities, towns, nations) not originally threatened by the impact will have to accept a temporary risk in the process of eliminating the threat to everyone. This unavoidable feature of a deflection thereby creates a host of extremely challenging social and geopolitical decisions.
The complexity of addressing these challenges invites creative and innovative solutions. They are technical, legal, political, social, and even ethical and philosophical. While many of the technical elements of PD have been addressed over the past two decades, most of the sociopolitical issues have only just come to be realized, let alone resolved. Indeed many of the likely sociopolitical issues have yet to be discovered.