Explosive volcanic eruptions inject hot mixtures of solid particles (tephra) and gasses into the atmosphere. Entraining ambient air, these mixtures can form plumes rising tens of kilometers until they spread laterally, forming umbrella clouds. While the largest clasts tend to settle in proximity to the volcano, the smallest fragments, commonly referred to as ash (≤2 mm in diameter), can be transported over long distances, forming volcanic clouds. Tephra plumes and clouds pose significant hazards to human society, affecting infrastructure, and human health through deposition on the ground or airborne suspension at low altitudes. Additionally, volcanic clouds are a threat to aviation, during both high-risk actions such as take-off and landing and at standard cruising altitudes. The ability to monitor and forecast tephra plumes and clouds is fundamental to mitigate the hazard associated with explosive eruptions. To that end, various monitoring techniques, ranging from ground-based instruments to sensors on-board satellites, and forecasting strategies, based on running numerical models to track the position of volcanic clouds, are efficiently employed. However, some limitations still exist, mainly due to the high unpredictability and variability of explosive eruptions, as well as the multiphase and complex nature of volcanic plumes. In the next decades, advances in monitoring and computational capabilities are expected to address these limitations and significantly improve the mitigation of the risk associated with tephra plumes and clouds.