For example, kinetic intercept ("bullet hitting a bullet") is surprisingly simple and has been a solved problem for several decades. People think it is hard because they literally imagine shooting down a bullet with another bullet, as if the missile was flying blind. Terminal guidance for these cases is computationally trivial -- modern hypersonic kinetic intercept platforms literally use 80486 class processors as guidance computers. Computers are much faster than the fundamental limitations of physics allow the world to change.
Almost all of the true design challenges are materials engineering problems. State-of-the-art weapon systems often operate at the edge of what is known to be possible with ordinary molecular materials, even highly exotic ones. There are severe restrictions on maneuverability when the system is already operating under material failure. In-atmosphere hypersonic platforms are already undergoing controlled disintegration during flight, even small excess stress will cause catastrophic failure of system components.
There is a second set of challenges around extreme throughput data processing in modern sensor-heavy weapon platforms (e.g. F-35) but these are essentially theoretical computer science or exotic DS&A problems.