This was a report on recent work of Michael Batanin. The goal of his work is to provide an environment for defining the concepts associated with weak ω-categories and for developing the ensuing theory. The approach is "globular". The talk was a trial run for two invited lectures at the Conference on Higher Category Theory and Mathematical Physics, Northwestern University (Evanston, Illinois; 28-30 March 1997). All that is correct is Batanin's; all errors are mine.