Declines in physical performance and cognition are commonly observed in older adults. The geroscience paradigm posits that a set of processes and pathways shared among age-associated conditions may also serve as a molecular explanation for the complex pathophysiology of physical frailty, sarcopenia, and cognitive decline. Mitochondrial dysfunction, inflammation, metabolic alterations, declines in cellular stemness, and altered intracellular signaling have been observed in muscle aging. Neurological factors have also been included among the determinants of sarcopenia. Neuromuscular junctions (NMJs) are synapses bridging nervous and skeletal muscle systems with a relevant role in age-related musculoskeletal derangement. Patterns of circulating metabolic and neurotrophic factors have been associated with physical frailty and sarcopenia. These factors are mostly related to disarrangements in protein-to-energy conversion as well as reduced calorie and protein intake to sustain muscle mass. A link between sarcopenia and cognitive decline in older adults has also been described with a possible role for muscle-derived mediators (i.e., myokines) in mediating muscle–brain crosstalk. Herein, we discuss the main molecular mechanisms and factors involved in the muscle–brain axis and their possible implication in cognitive decline in older adults. An overview of current behavioral strategies that allegedly act on the muscle–brain axis is also provided.