Neurofeedback based on real-time functional magnetic resonance imaging (rt-fMRI) is a novel and rapidly developing research field. It allows for training of voluntary control over localized brain activity and connectivity and has demonstrated promising clinical applications. Because of the rapid technical developments of MRI techniques and the availability of high-performance computing, new methodological advances in rt-fMRI neurofeedback become possible. Here we outline the core components of a novel open-source neurofeedback framework, termed Open NeuroFeedback Training (OpenNFT), which efficiently integrates these new developments. This framework is implemented using Python and Matlab source code to allow for diverse functionality, high modularity, and rapid extendibility of the software depending on the user's needs. In addition, it provides an easy interface to the functionality of Statistical Parametric Mapping (SPM) that is also open-source and one of the most widely used fMRI data analysis software. We demonstrate the functionality of our new framework by describing case studies that include neurofeedback protocols based on brain activity levels, effective connectivity models, and pattern classification approaches. This open-source initiative provides a suitable framework to actively engage in the development of novel neurofeedback approaches, so that local methodological developments can be easily made accessible to a wider range of users.