Aging is accompanied by several changes which may affect swallowing function. The beginning of these changes, termed presbyphagia, still captures a preserved swallowing function, although burdened by the consequences of the physiological aging process. Several stressors (including diseases and medications) can easily trigger the disruption of this (increasingly weak) equilibrium and lead to overt dysphagia. It is noteworthy that the swallowing dysfunction may be aggravated by the sarcopenic process, characterizing the so-called “sarcopenic dysphagia”, potentially responsible for several health-related negative outcomes. The assessment and management of sarcopenic dysphagia largely rely on the evaluation and integrated treatment of both constituting conditions (i.e., sarcopenia and dysphagia). The management of dysphagia requires a multidimensional approach and can be designed as either compensatory (aimed at producing immediate benefit for the patient through postural adjustments, swallowing maneuvers, and diet modifications) or rehabilitative. Interestingly, some evidence suggests that resistance training traditionally applied to tackle the lower extremity in sarcopenia may be simultaneously beneficial for sarcopenic dysphagia. If these preliminary results (discussed in the present review article) will be confirmed, the systemic beneficial effects of physical exercise will be indirectly demonstrated. This will also support the need of promoting healthy lifestyle in all sarcopenic individuals (thus potentially at risk of dysphagia).