In its many embodiments, the present invention provides provides certain S-imino-S-oxo iminothiadiazine compounds, including compounds Formula (I): or a tautomers and/or stereoisomers thereof, and pharmaceutically acceptable salts of said compounds, said tautomeros and said stereoisomers, wherein RN, R1, R2, R3, R4, ring A, RA, m, L1, and RL are as defined herein. The novel compounds of the invention are useful as BACE inhibitors and may be useful for the treatment and prevention of various pathologies related thereto. Pharmaceutical compositions comprising one or more such compounds (alone and in combination with one or more other active agents), and methods for their preparation and use, including for the possible treatment of Alzheimer's disease, are also disclosed.