A primary goal of volcanology is forecasting hazardous eruptive activity. Despite much progress over the last century, however, volcanoes still erupt with no detected precursors, lives and livelihoods are lost to eruptive activity, and forecasting the onsets of eruptions remains fraught with uncertainty. Long-term forecasts are generally derived from the geological and historical records, from which recurrence intervals and styles of activity can be inferred, while shorter-term forecasts are derived from patterns in monitoring data. Information from geology and monitoring data can be evaluated and combined using statistical analysis, expert elicitation, and conceptual and or mathematical models. Integrative frameworks, such as event trees, combine this diversity of information to produce probabilistic forecasts that can inform the style and scale of the societal response to a potential future eruption. Several developments show promise to revolutionize the utility and accuracy of these forecasts. These include growth in the quantity and quality of multidisciplinary monitoring data, coupled with increases in computing power; machine learning algorithms, which will allow far better utilization of this growing volume of data; and new physiochemical volcano models and data assimilation algorithms, which take advantage of a wide range of monitoring data and realistic physics to better predict the evolution of a given physical state. Although eruption forecasts may never be as generally reliable as weather forecasts, and great caution must be exercised when attempting to predict highly complex volcanic behavior, these and other innovations-particularly when combined in integrative, fully probabilistic forecasting frameworks-should help volcanologists to better issue warnings of volcanic activity on societally relevant time frames.