The knot classification problem is one of the most important problems on the boundary of pure and applied mathematics. A famous theorem of Markov showed that this can be approached via combinatorial group theory. The Markov problem must be solved in two stages: The conjugacy problem must be solved in each member of a family of groups and then a combinatorial problem in their union must be solved. The question of whether the first can be done efficiently is an important question first raised in 1969 by Garside who presented the first solution (albeit inefficient) to this problem. Many people have published solutions to the problem but all inefficient. This talk will introduce the first efficient solution which puts the practical classification of knots back on the drawing board. It will be outlined how the method can be used for a wide class of groups and not just for the braid groups.