Nowadays, event processing is becoming the backbone of many applications. Therefore, it is necessary to provide suitable abstractions to properly modularize the concerns that appear in event-driven applications. We identify four categories of languages that support event-driven programming, and identify their shortcomings in achieving modularity in the implementation of applications. We propose gummy modules and their implementation in the GummyJ language as a solution. Gummy modules have well-defined event-based interfaces, and can have a primitive or a composite structure. Composite gummy modules are means to group a set of correlated event processing concerns and restrict the visibility of events among them. We provide an example usage of gummy modules, and discuss their event processing semantics.