There are numerous possibilities and motivations for an adaptive BCI, which may not be easy to clarify and organize for a newcomer to the field. To our knowledge, there has not been any work done in classifying the literature on adaptive BCI in a comprehensive and structured way. We propose a conceptual framework, a taxonomy of adaptive BCI methods which encompasses most important approaches to fit them in such a way that a reader can clearly visualize which elements are being adapted and for what reason. In the interest of having a clear review of existing adaptive BCIs, this framework considers adaptation approaches for both the user and the machine, i.e., using instructional design observations as well as the usual machine learning techniques. This framework not only provides a coherent review of such extensive literature but also enables the reader to perceive gaps and flaws in the current BCI systems, which would hopefully bring novel solutions for an overall improvement.