Recent progress in "on-the-fly" trajectory simulations of molecular reactions, using different electronic structure methods is discussed, with analysis of the insights that such calculations can provide and of the strengths and limitations of the algorithms available. New developments in the use of both ab initio and semi-empirical electronic structure algorithms are described. The emphasis is on: (i) calculations of electronic properties along the reactive trajectories and the unique insights this can contribute to the processes; (ii) electronic structure methods recently introduced to this topic to improve accuracy, extend applicability or enhance computational efficiency. The methods are presented with examples, including new results, of reactions of both isolated molecules and of molecules in media, mostly clusters. Possible future directions for this fast growing field are suggested.