The Binaural Rendering Toolbox (BRT) is a set of software libraries, applications, and definitions aimed as a virtual laboratory for psychoacoustic experimentation. The BRT is developed in the framework of the SONICOM project (www.sonicom.eu) and will include the algorithms developed in the 3D Tune-In Toolkit (https://github.com/3DTune-In/3dti_AudioToolkit) in a new open, extensible architecture. At the core of the BRT Toolbox, a library provides C++ implementations of listener models, source models, and environment models, including a growing collection of portings to different audio frameworks such as PureData, MaxMSP and VST plugins, by means of the Avendish library. In addition, the BRT also includes an application controlled via the Open Sound Control (OSC) protocol. This paper describes the architecture of the BRT, its main features, and how to apply it to conduct psychoacoustic experiments such that, when sharing the used configuration, their reproducibility is facilitated. Moreover, the toolbox provides a complete trace of the experiment including the delivered binaural audio, annotated with the listener and source movements. For this purpose, a new convention of SOFA is proposed to store dynamic measurements, facilitating their use in the Auditory Model Toolbox (AMT).