The requirements for ever-increasing volumes of data storage have urged intensive studies to find feasible means to satisfy them. In the long run, new device concepts and technologies that overcome the limitations of traditional CMOS-based memory cells will be needed and adopted. In the meantime, there are still innovations within the current CMOS technology, which could be implemented to improve the data storage ability of memory cells—e.g., replacement of the current dominant floating gate non-volatile memory (NVM) by a charge trapping memory. The latter offers better operation characteristics, e.g., improved retention and endurance, lower power consumption, higher program/erase (P/E) speed and allows vertical stacking. This work provides an overview of our systematic studies of charge-trapping memory cells with a HfO2/Al2O3-based charge-trapping layer prepared by atomic layer deposition (ALD). The possibility to tailor density, energy, and spatial distributions of charge storage traps by the introduction of Al in HfO2 is demonstrated. The impact of the charge trapping layer composition, annealing process, material and thickness of tunneling oxide on the memory windows, and retention and endurance characteristics of the structures are considered. Challenges to optimizing the composition and technology of charge-trapping memory cells toward meeting the requirements for high density of trapped charge and reliable storage with a negligible loss of charges in the CTF memory cell are discussed. We also outline the perspectives and opportunities for further research and innovations enabled by charge-trapping HfO2/Al2O3-based stacks.