Helicobacter pylori is a persistent gastric pathogen associated with chronic gastritis, peptic ulcer disease, gastric mucosa-associated lymphoid tissue lymphoma, and non-cardia gastric cancer. Although eradication can prevent important clinical outcomes, increasing resistance to clarithromycin, metronidazole, and fluoroquinolones has undermined historically successful empirical regimens. This narrative review critically examines the biological and clinical drivers of eradication failure, current resistance-aware therapeutic approaches, and emerging diagnostic and treatment strategies. Evidence was selected from major international guidelines, systematic reviews, clinical trials, and recent translational studies, with emphasis on literature published between 2022 and 2026. Contemporary recommendations prioritize optimized 14-day bismuth quadruple therapy when susceptibility is unknown, while rifabutin-based regimens and vonoprazan-amoxicillin dual therapy offer alternatives for selected patients. Molecular resistance testing, adequate acid suppression, treatment adherence, and systematic confirmation of eradication are central to precision management. Probiotics may reduce adverse effects in some settings but cannot replace antimicrobial therapy. Antimicrobial peptides, biofilm-disrupting compounds, targeted delivery systems, bacteriophage-derived approaches, and vaccines remain largely investigational. Future progress will depend on integrating locally relevant resistance surveillance, validated susceptibility testing, antimicrobial stewardship, and equitable access to effective regimens. This review provides a practical synthesis of established strategies and emerging opportunities while emphasizing the need to distinguish clinical evidence from preclinical promise.