Brain-computer interfaces (BCIs) translate brain activity into digital commands for interaction with the physical world. The technology has great potential in several applied areas, ranging from medical applications to entertainment industry, and creates new conditions for basic research in cognitive neuroscience. The BCIs of today, however, offer only crude online classification of the user's current state of mind, and more sophisticated decoding of mental states depends on time-consuming offline data analysis. The present paper addresses this limitation directly by leveraging a set of improvements to the analytical pipeline to pave the way for the next generation of online BCIs. Specifically, we introduce an open-source research framework that features a modular and customizable hardware-independent design. This framework facilitates human-in-the-loop (HIL) model training and retraining, real-time stimulus control, and enables transfer learning and cloud computing for the online classification of electroencephalography (EEG) data. Stimuli for the subject and diagnostics for the researcher are shown on separate displays using web browser technologies. Messages are sent using the Lab Streaming Layer standard and websockets. Real-time signal processing and classification, as well as training of machine learning models, is facilitated by the open-source Python package Timeflux. The framework runs on Linux, MacOS, and Windows. While online analysis is the main target of the BCI-HIL framework, offline analysis of the EEG data can be performed with Python, MATLAB, and Julia through packages like MNE, EEGLAB, or FieldTrip. The paper describes and discusses desirable properties of a human-in-the-loop BCI research platform. The BCI-HIL framework is released under MIT license with examples at:bci.lu.se/bci-hil(or at:github.com/bci-hil/bci-hil).