Are we talking about boost phase, midcourse or terminal phase defense?
In all of these cases, a successful intercept will happen tens if not thousands of kilometers from the target.
A boost phase interception would happen above the launch area. A midcourse intercept would essentially happen in space and a terminal intercept would happen at the edge of the atmosphere.
I'd recommend reading about Aegis, THAAD and GMD. Also see https://en.wikipedia.org/wiki/Ballistic_missile_flight_phase...
Of course there are also stealth bombers and cruise missiles. In the case of stealth bombers, you either shoot them before the bombs are dropped or you don't (Barring some extremely conveniently located point defenses, like C-RAM)
Cruise missiles? Shot down by conventional air defenses hundreds of kilometers from the target if terrain allows.
Hypersonic cruise missiles? Maybe shot down by conventional air defenses.