Immunization substantially contributes to global health by saving millions of lives every year. Yet, a vast amount of people around the world, including nearly 20 to 25 million infants each year, have insufficient access to vaccines. Challenges related to the storage and distribution of vaccines persist, contributing to vaccination coverage rates that are below the required thresholds to reach herd immunity. Our research is motivated and based on the challenges faced by health supply chain practitioners and the potential solutions put forward by the development sector. We start by giving an overview of the main characteristics and challenges inherent to vaccine supply chains in low- and middle-income countries and compare the issues reported in practice to those investigated in the operations research/operations management literature. In many low- and middle-income countries, the distribution of vaccines is burdensome due to, among others, bad road conditions. In addition, the accessibility of various roads is further reduced or eliminated during the rainy season, leaving numerous facilities cut off from the road network for months. Using the context of the Malagasy vaccine supply chain, we develop a modeling approach to assess and mitigate the effect of the rainy season on vaccination coverage and inequities in low- and middle-income countries. Recently, drones are increasingly being put forward as an emerging technology that might provide a solution to the logistical challenges in health supply chains in low- and middle-income countries. However, limited research has been done on the use of medical drone deliveries. We therefore model and investigate the impact of different types of drones on the trade-off between vaccination coverage and equity, and apply our model to the context of the Malagasy vaccine supply chain. Next, widening our focus from vaccines to health products in general, we use semi-structured interviews to gain a deeper understanding about the challenges related to the implementation of drones for transporting medical supplies in low- and middle-income countries.