Background: Peru is an upper-middle-income country with wide social and regional disparities. In recent years, sustained multisectoral antipoverty programmes involving governments, political parties, and civil society have included explicit health and nutrition goals and spending increased sharply. We did a country case study with the aim of documenting Peru's progress in reproductive, maternal, neonatal, and child health from 2000-13, and explored the potential determinants. Methods: We examined the outcomes of health interventions coverage, under-5 mortality, neonatal mortality, and prevalence of under-5 stunting. We obtained data from interviews with key informants, a literature review of published and unpublished data, national censuses, and governmental reports. We obtained information on social determinants of health, including economic growth, poverty, unmet basic needs, urbanisation, women's education, water supply, fertility rates, and child nutrition from the annual national households surveys and the Peruvian Demographic and Health Surveys. We obtained national mortality data from the Interagency Group for Child Mortality Estimation, and calculated subnational rates from 11 surveys. Analyses were stratified by region, wealth quintiles, and urban or rural residence. We calculated coverage indicators for the years 2000-13, and we used the Lives Saved Tool (LiST) to estimate the effect of changes in intervention coverage and in nutritional status on mortality. Findings: From 2000 to 2013, under-5 mortality fell by 58% from 39·8 deaths per 1000 livebirths to 16·7. LiST, which was used to predict the decline in mortality arising from changes in fertility rates, water and sanitation, undernutrition, and coverage of indicators of reproductive, maternal, neonatal, and child health predicted that the under-5 mortality rate would fall from 39·8 to 28·4 per 1000 livebirths, accounting for 49·2% of the reported reduction. Neonatal mortality fell by 51% from 16·2 deaths per 1000 livebirths to 8·0. Stunting prevalence remained stable at around 30% until 2007, decreasing to 17·5% by 2013, and the composite coverage index for essential health interventions increased from 75·1% to 82·6%, with faster increases among the poor, in rural areas, and in the Andean region. Socioeconomic, urban-rural, and regional inequalities in coverage, mortality, and stunting were substantially reduced. The proportion of the population living below the poverty line reduced from 47·8% to 23·9%, women with fewer than 4 years of schooling reduced from 11·5% to 6·9%, urbanisation increased from 68·1% to 75·6%, and the total fertility rate decreased from 3·0 children per woman to 2·4. We interviewed 175 key informants and they raised the following issues: economic growth, improvement of social determinants, civil society empowerment and advocacy, out-of-health and within-health-sector changes, and sustained implementation of evidence-based, pro-poor reproductive, maternal, neonatal, and child health interventions. Interpretation: Peru has made substantial progress in reducing neonatal and under-5 mortality, and child stunting. This country is a good example of how a combination of political will, economic growth, broad societal participation, strategies focused on poor people, and increased spending in health and related sectors can achieve significant progress in reproductive, maternal, neonatal, and child health. The remaining challenges include continuing to address inequalities in wealth distribution, poverty, and access to basic services, especially in the Amazon and Andean rural areas. Funding: Bill & Melinda Gates Foundation.