The present invention pertains generally to the field of therapeutic compounds, and more specifically to certain aryl-amido-aryl compounds of the following formula (for convenience, collectively referred to herein as &ldquoAAA compounds&rdquo), which, inter alia, are (selective) retinoic acid receptor &alpha (RAR&alpha) agonists. The present invention also pertains to pharmaceutical compositions comprising such compounds, and the use of such compounds and compositions, both in vitro and in vivo, to (selectively) activate RAR&alpha, and in the treatment of diseases and conditions that are mediated by RAR&alpha, that are ameliorated by the activation of RAR&alpha, etc., including cognitive disorders, memory impairment, memory deficit, senile dementia, Alzheimers disease, early stage Alzheimers disease, intermediate stage Alzheimers disease, late stage Alzheimers disease, cognitive impairment, and mild cognitive impairment.