Burnside groups and small cancellation theory

The Novikov-Adian theorem states that a non-cyclic Burnside group B(m,n) of odd exponent n greater or equal 665 is infinite. Starting from the original approach, all known proofs of infiniteness of B(m,n) utilize the idea that the group can be described in terms of some iterated small cancellation condition. In the last decade, several explicit implementations of small cancellation conditions of this type were introduced which can be applied also in a more general setup to groups acting on hyperbolic metric spaces. I will give a brief overview of the small cancellation approach to Burnside groups and describe yet another implementation providing a reasonably accessible proof that B(m,n) is infinite with rather moderate bound n > 2000 on the odd exponent n.