In the 50's and 60's, when anti aircraft missile technology was blooming, many designs used ramjet engines brought up to operating speed by rockets. This seems like a good idea, since ramjets have significantly higher specific impulse than rockets, increasing their range. Over decades however, it seems that the concept has been discarded in favor of pure rockets, with exception of anti shipping missiles. What could be the considerations that made engineers favor pure rockets?
I have worked on the edge of this technology. the simple answer is the performance of the scram jet doesn't make uo for the added weight of the system. The most recent work NASA has performed was the HYPER-X program, try this link.