Despite major reductions in child mortality, decrease in neonatal (first month of life) deaths has been substantially slower. To further reduce neonatal deaths, scale-up of relevant and timely health interventions is necessary. Such scale-up needs to be supported by evidence, but important gaps remain in our knowledge regarding the timing and causes of neonatal deaths. Birth and the days immediately following carry the highest daily risk of death, yet standard life tables do not present daily mortality risks within the neonatal period. Around three-quarters of neonatal deaths occur during the first week, and most interventions to prevent these deaths must be delivered very quickly. Thus, understanding the neonatal day-of-death distribution is important for delivering appropriate and timely interventions. We fitted an exponential function to survey data to model the daily neonatal mortality risk, focusing on the first day and week after birth. Using this model and observed data, we estimated the daily risk of death in the neonatal period for 186 countries in 2013. Targeted interventions also require reliable estimates of neonatal cause-of-death distributions. Cause-of-death estimation is challenging because of limited data quantity and quality in many countries. Previous work highlighted the need to expand the existing country-specific neonatal cause-of-death estimates and improve the methods. We developed a multinomial model to estimate the neonatal cause-of-death distribution by the early (days 0-6) and late (days 7-27) neonatal periods. We then focused on methodological improvements, including evaluating performance and developing a proof-of-concept Bayesian mixed effects model. This thesis straddles two topics that are receiving increased attention: cause-of-death estimation and neonatal health. Ideally, the results from this work can help current neonatal health policies and programmes while contributing to the growing area of cause-of-death modelling. However, the longer-term aim should be to improve data collection to obviate the need for statistical modelling exercises.