In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning tree after dynamic changes like edge weight changes, rather than having to recompute it from scatch each time. The first part of the paper surveys various algorithms available today both in sequential and distributed environments to solve static MST problem. We also present some of the efficient sequential algorithms for computing dynamic MST like the Frederickson's algorithm and Eppstein's sparsification technique. Lastly we present our new sequential and distributed algorithms for dynamic MST problem. To our knowledge, this is the first of the distributed algorithms for computing dynamic MSTs.