Recent years have seen an increase in the popularity of multivariate pattern (MVP) analysis of functional magnetic resonance (fMRI) data, and, to a much lesser extent, magneto- and electro-encephalography (M/EEG) data. We present CoSMoMVPA, a lightweight MVPA (MVP analysis) toolbox implemented in the intersection of the Matlab and GNU Octave languages, that treats both fMRI and M/EEG data as first-class citizens. CoSMoMVPA supports all state-of-the-art MVP analysis techniques, including searchlight analyses, classification, correlations, representational similarity analysis, and the time generalization method. These can be used to address both data-driven and hypothesis-driven questions about neural organization and representations, both within and across: space, time, frequency bands, neuroimaging modalities, individuals, and species. It uses a uniform data representation of fMRI data in the volume or on the surface, and of M/EEG data at the sensor and source level. Through various external toolboxes, it directly supports reading and writing a variety of fMRI and M/EEG neuroimaging formats, and, where applicable, can convert between them. As a result, it can be integrated readily in existing pipelines and used with existing preprocessed datasets. CoSMoMVPA overloads the traditional volumetric searchlight concept to support neighborhoods for M/EEG and surface-based fMRI data, which supports localization of multivariate effects of interest across space, time, and frequency dimensions. CoSMoMVPA also provides a generalized approach to multiple comparison correction across these dimensions using Threshold-Free Cluster Enhancement with state-of-the-art clustering and permutation techniques. CoSMoMVPA is highly modular and uses abstractions to provide a uniform interface for a variety of MVP measures. Typical analyses require a few lines of code, making it accessible to beginner users. At the same time, expert programmers can easily extend its functionality. CoSMoMVPA comes with extensive documentation, including a variety of runnable demonstration scripts and analysis exercises (with example data and solutions). It uses best software engineering practices including version control, distributed development, an automated test suite, and continuous integration testing. It can be used with the proprietary Matlab and the free GNU Octave software, and it complies with open source distribution platforms such as NeuroDebian. CoSMoMVPA is Free/Open Source Software under the permissive MIT license. Website: http://cosmomvpa.org Source code: https://github.com/CoSMoMVPA/CoSMoMVPA