Paul Martin: Reference Section
The non-crossing idea involves drawing diagrams on a rectangle. It is natural (particularly from a computational physics perspective) to consider a generalisation where one draws diagrams on a cylinder, and distinguishes closed loops (formed in diagram composition) that are non-contractible. Rather than address this algebra directly, it is convenient to study an algebra in which the cohomological data is encoded in a blob on the `seam' (a line drawn on the cylinder to cut it open, and hence return to the rectangle). This is the idea of the blob algebra. (Although it can also be characterised in a number of other interesting ways...)
One of the most interesting aspects of the study of the blob algebra concerns its representation theory. Its `reductive' representation theory over algebraically closed fields is quite completely understood (see [Cox et al] and references therein). But a number of other interesting questions about it and its generalisations remain open.
Some nice looking recent papers on the blob algebra, indicating a lot of interesting open problems (!):