Continued downscaling of semiconductor devices has placed stringent constraints on all aspects of the fabrication process including plasma-assisted anisotropic etching. To address manufacturing challenges associated with atomic-scale control, material selectivity, etch fidelity, and increasingly complex device architectures, reactive ion etching (RIE) is transitioning to plasma-assisted atomic layer etching (ALE). Even though the number of elements used in the semiconductor devices has increased several-fold over the last four decades, SiO2 and SiNx remain the most commonly used dielectric materials. In fact, fluorocarbon based, plasma-assisted ALE processes for SiO2 and SiNx have already been integrated into semiconductor manufacturing, including etching of self-aligned contacts for advanced transistors. However, several challenges remain in achieving ultrahigh etch selectivity of SiO2 over SiNx and vice versa. In this article, first, the authors provide a focused review on selective RIE of SiO2 over SiNx and contrast this with ALE. A particular focus is given to the etching mechanism, including the role of the mixing layer composition and thickness at the fluorocarbon-SiO2 interface, the F-to-C ratio in the fluorocarbon parent gas, H2 dilution, surface composition on the nonetched SiNx, ion flux and energy, Ar plasma activation duration in ALE, and chamber memory effects. Second, we discuss the reverse case of selectively etching SiNx over SiO2 with careful attention given to the role of novel hydrofluorocarbon gases and dilution of the primary feed gas with other gases such as CH4 and NO. In the second part of this review, we also discuss how novel surface chemistries are enabled by the introduction of ALE, which include selective (NH4)2SiF6 formation on the SiNx surface and selective surface prefunctionalization of SiO2 to enable ultrahigh selectivity. Through this review, the authors hope to provide the readers with an exhaustive knowledge of the selectivity mechanisms for RIE of SiO2 over SiNx and vice versa, which provides a basis for developing future highly material-selective ALE processes.