What missile defense systems would be used against hypersonic glide vehicles and cruise missiles (like Avangard or Sky Star)? What challenges would nations face developing them?
From an aeronautical point of view, an interceptor normally must be faster than the target it is seeking to reach. Therefore, existing missile defense systems are ineffective against hypersonic aircraft, because the target is moving at least as fast as the would-be interceptor.
Of course, if the target moves in a unchanging straight line, then it is theoretically possible for the interceptor to reach it, so long as it is positioned in front of the target. For this exact reason, all hypersonic missiles are designed to make irregular movements in any situation where an interceptor may be present.
For straight line paths, there is a cone of viability where an interceptor needs to be in order to intercept the target. The slower the interceptor is, the smaller this cone becomes. In the current (2020) strategic situation, the cone of intercept for existing hypersonic weapons is so small that the probability of intercept is impractically small, even for high value targets. This is one reason why there is a great effort currently to develop laser-based defensive systems.