Christensen divides new technologies into two groups: sustaining and disruptive. Sustaining technology helps improve a product for its current customers for example Intel building a faster microprocessor. Disruptive technology is technology that is not initially useful for a big company's current clients. So other newer and smaller companies develop the technology for a niche market. But eventually the technology improves to meet the needs of the original big company's customers at a much lower cost. At this time the big company cannot catch up with the new technology and loses their main business to the newer startups. Christensen gives many examples such as the development of smaller disk drives and the advent of discount stores like Target hurting bigger retailers like Sears.
The book makes some solid arguments but determining which technologies will be disruptive is quite difficult. So companies need to place lots of bets perhaps why NEC funds quantum computing research just in case it becomes a disruptive technology in the future.
Do the same concepts apply to research? In complexity we have had some disruptive technologies, for example, the PCP theorem for hardness of approximation or the idea of Nisan and Wigderson of using hard languages to derandomize, or going way back the whole concept of NP-completeness. Other concepts like circuit complexity have not been as disruptive as originally thought. Also one could view tools like the probabilistic method or extractors as disruptive.
What could happen to large companies can also happen to researchers. Suppose George is a researcher who creates new results building on current ideas with small twists (sustaining technology). George ignores some new ideas in complexity because it doesn't seem to help him prove new results in his area. But as those new technologies develop they later allow others to go well beyond what George has done. Now George is behind the curve on the new disruptive technology and can no longer play an important role even in his own field.
What can George do? He can learn the new techniques or he can change fields. And often the newcomers never properly learn the old tools and George can still pull a few surprises out of his hat.