Charge-trapping nonvolatile memories based on amorphous oxide semiconductor (AOS) thin-film transistors (TFTs) present unique merits for next-generation flexible and transparent electronic systems; however, the memory devices still face some challenges, such as a high power consumption, a low operating speed, and insufficient data retention. The technology of atomic layer deposition (ALD) with many advantages is expected to overcome the challenges. In this perspective, the ALD fabrication processes and electrical characteristics of the AOS TFT memories are reviewed from the viewpoint of the device components, including a charge storage layer, charge blocking/tunneling layers, and an active channel layer. Meanwhile, for improving the performance of the memory devices, engineering of device structures, materials, and processes is further discussed by combining with the ALD technique.