Today the influence of non-volatile solid-state memories on persons' lives has become more prominent because of their non-volatility, low data latency, and high robustness. As a pioneering technology that is representative of non-volatile solidstate memories, flash memory has recently seen widespread application in many areas ranging from electronic appliances, such as cell phones and digital cameras, to external storage devices such as universal serial bus (USB) memory. Moreover, owing to its large storage capacity, it is expected that in the near future, flash memory will replace hard-disk drives as a dominant technology in the mass storage market, especially because of recently emerging solid-state drives. However, the rapid growth of the global digital data has led to the need for flash memories to have larger storage capacity, thus requiring a further downscaling of the cell size. Such a miniaturization is expected to be extremely difficult because of the well-known scaling limit of flash memories. It is therefore necessary to either explore innovative technologies that can extend the areal density of flash memories beyond the scaling limits, or to vigorously develop alternative non-volatile solid-state memories including ferroelectric random-access memory, magnetoresistive random-access memory, phase-change random-access memory, and resistive random-access memory. In this paper, we review the physical principles of flash memories and their technical challenges that affect our ability to enhance the storage capacity. We then present a detailed discussion of novel technologies that can extend the storage density of flash memories beyond the commonly accepted limits. In each case, we subsequently discuss the physical principles of these new types of non-volatile solid-state memories as well as their respective merits and weakness when utilized for data storage applications. Finally, we predict the future prospects for the aforementioned solid-state memories for the next generation of data-storage devices based on a comparison of their performance.