Although networks provide a powerful approach to study a large variety of ecological systems, their formulation does not typically account for multiple interaction types, interactions that vary in space and time, and interconnected systems such as networks of networks. The emergent field of 'multilayer networks' provides a natural framework for extending analyses of ecological systems to include such multiple layers of complexity, as it specifically allows one to differentiate and model 'intralayer' and 'interlayer' connectivity. The framework provides a set of concepts and tools that can be adapted and applied to ecology, facilitating research on high-dimensional, heterogeneous systems in nature. Here, we formally define ecological multilayer networks based on a review of previous, related approaches; illustrate their application and potential with analyses of existing data; and discuss limitations, challenges, and future applications. The integration of multilayer network theory into ecology offers largely untapped potential to investigate ecological complexity and provide new theoretical and empirical insights into the architecture and dynamics of ecological systems.