Cervical cancer disproportionately affects low-resource settings. Papanicolaou, human papillomavirus (HPV), and visual inspection of cervix with acetic acid (VIA) testing, each with different characteristics, will reduce cervical cancer burden. We conducted a critical literature review using PubMed, Cochrane, WHO, and grey literature from 1994 to 2020. We examined efficacy, harms, and comparative effectiveness of screening methods by age, human immunodeficiency virus, provider characteristics, and assessed implementation challenges in low-resource settings. Comprehensive data on utility and efficacy of screening tests indicates that each screening has strengths and shortcomings but all confer acceptable performance. HPV and VIA appear more promising. Primary HPV test-and-treat, self-testing, and co-testing have been studied but data on triage plans, cost, support system, implementation and sustainability is unclear in low-resource settings. HPV testing could help target subgroups of older or higher risk women. VIA offers local capacity-building and scalability. Quality VIA technique after HPV testing is still required to guide post-screening treatments. VIA competencies decline gradually with current standard trainings. Stationary cervicography improves VIA quality but isn't scalable. Affordable smartphones eliminate this barrier, enhance training through mentorship, and advance continuing education and peer-to-peer training. Smartphone-based VIA facilitates cervical image storage for patient education, health promotion, record-keeping, follow-up care, remote expert support, and quality control to improve VIA reliability and reproducibility and reduce mis-diagnoses and burden to health systems. Rather than ranking screening methods using test characteristics alone in study or higher-resource settings, we advocate for scalable strategies that maximize reliability and access and reduce cost and human resources.