The macroscopic fluctuation theory (MFT) was developed by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim for the description of nonequilibrium steady states in simple lattice gases. Later on the MFT was extended, by Derrida and Gerschenfeld and by other workers, to time-dependent problems, and also employed for the description of macroscopic fluctuations in a host of settings which involve large ensembles of interacting particles. Close connections were established, by Tailleur, Kurchan and Lecomte, and by other workers, between the MFT and the optimal fluctuation method (also known as the weak noise theory or instanton method). Numerical and analytical techniques have been developed for solving the nonlinear partial differental equations of the MFT. I will give a brief introduction to some of these developments.