We describe ModSpec, a MATLAB/Octave based specification format suitable for modelling devices across a wide variety of application domains, including circuits, optics, fluidics and biology. The ModSpec format and associated API are centered around describing the nonlinear differential equations at the core of any device model. The format is open, general and easy to use, and is supported by toolchains that translate and automatically differentiate models, set up equations for systems of interacting devices, and provide simulation facilities. We illustrate the use of ModSpec for modelling semiconductor, photovoltaic, fluidic and neuronal devices and systems.