The results of the work that I have carried out are presented in three chapters.

The main focus of Chapter 2 is on double-ended methods for finding transition states. A detailed review of one of the leading methods from that class is followed by the discussion of our modifications and improvements that allowed us to extend its applicability. Results for a model two-dimensional surface and Lennard-Jones clusters of several sizes are presented. The chapter culminates with an application to finding folding paths for a family of small peptides known as tryptophan zippers.

Chapter 3 is devoted to discussion of two exciting properties of rearrangement pathways -- cooperativity and localisation. A new measure of cooperativity suitable for applications to atomic rearrangements is introduced and subsequently used to establish the links between cooperativity of a single-step rearrangement, the energy barrier height and the difficulty of locating the corresponding transition state with both single-ended and double-ended methods.

In Chapter 4 we deal with compact representations of large pathway ensembles borrowing ideas from graph theory and the theory of random processes. The main theme is the development of faster methods for calculation of mean escape times for graphs of increasing complexity. We devise a number of approaches for extracting this kinetic information and compare them to well-established techniques such as kinetic Monte Carlo and discrete path sampling.

Chapter 5 summarises the achievements of the work described in this thesis and suggests the directions for future research.