Neurodegenerative and neuropsychiatric disorders remain a major public health concern due to their progressive nature, high prevalence, and considerable socioeconomic burden. Conventional treatments often fall short, facing limitations such as pharmacoresistance, adverse effects, and limited efficacy, underscoring the need for complementary approaches. Recent advances highlight the central role of the gut–brain axis (GBA) in neurological health, positioning psychobiotics and probiotic strains with potential mental health benefits, as candidates in adjunctive therapy. This review integrates current evidence on the GBA’s involvement in conditions such as Alzheimer’s disease, Parkinson’s disease, depression, and anxiety. We examine how psychobiotics may modulate neuroinflammation, oxidative stress, and neurotransmitter signaling, thereby contributing to cognitive and emotional regulation. Both preclinical and clinical studies are discussed, with emphasis on biomarker changes, quality-of-life outcomes, and neuropsychiatric comorbidities. We also explore recent innovations, including precision psychobiotics, microbiota–drug synergies, and their relevance to overlapping metabolic and neurodegenerative pathologies. Finally, we address the major translational challenges in the field, strain selection, methodological standardization, biomarker integration, and ethical design, highlighting key perspectives for advancing psychobiotics research toward clinical application.