Background/Objectives: Chronic Obstructive Pulmonary Disease (COPD) is frequently associated with dyspnea, impaired health-related quality of life (HRQoL), and cognitive dysfunction. Although pulmonary rehabilitation (PR) is considered a core therapeutic strategy, its specific effects on cognitive function, dyspnea, and dysphonia remain unclear. This systematic review aimed to evaluate the impact of PR and respiratory or cognitive-focused rehabilitative interventions on dyspnea, quality of life, cognitive performance, and voice outcomes in adults with COPD. Methods: This review was conducted in accordance with PRISMA 2020 guidelines and registered in PROSPERO (CRD420251131325). A systematic search of PubMed, Scopus and Web of Science identified studies published between 2010 and 21 August 2025. Eligible designs included randomized and non-randomized controlled studies, cohort, and mixed-method studies involving adults with COPD undergoing rehabilitative interventions targeting dyspnea, cognition, dysphonia, or swallowing. Outcomes included cognitive measures, dyspnea scales, voice parameters, and HRQoL indices. Results: Twelve studies (n ≈ 810 participants) met inclusion criteria. Most PR and exercise-based programs showed improvements in global cognition and executive functions, particularly when combined with cognitive training or high-intensity exercise modalities. Dyspnea improved consistently following short- to medium-term PR or respiratory muscle training, whereas low-frequency long-term programs yielded limited benefit. HRQoL improved across structured PR programs, especially in multidimensional interventions. Only one study assessed dysphonia, reporting transient improvements in maximum phonation time following inspiratory muscle training. No included study evaluated dysphagia-related outcomes. Conclusions: PR and respiratory muscle training can enhance cognition, dyspnea, and HRQoL in COPD, although evidence for dysphonia remains scarce and dysphagia is entirely unaddressed. Future high-quality trials should adopt standardized outcome measures, include long-term follow-up, and integrate voice and swallowing assessments within PR pathways.