The ever‐increasing demand for higher‐capacity digital memory shows no sign of declining. The conventional strategy for meeting such demand, i.e. shrinking of the memory cell size, will no longer be useful at some point in the future, owing to economic reasons and performance degradation. Nevertheless, performance of computing systems will keep improving for the next generation information technology. This indicates the necessity to consider a fundamentally disparate approach to enhance memory technology. Here, the current status of computer memory chips is reviewed and the pros and cons of the present technology are discussed from computing system, fabrication technology, and materials points of view. Based on this knowledge, the limitations of the present technologies are described, and the possible solutions suggested up to now are reassessed. Finally, a shift in the fundamental computational paradigm from von Neumann computing to other alternatives such as neuromorphic computing and material implication, is commented upon.