Fusion neutronics is devoted to problems dealing with neutron and photon radiation transport in fusion reactor systems where 14 MeV source neutrons are generated through (d,t) fusion reactions in the plasma chamber and subsequently are transported through the surrounding matter. The Monte Carlo method is a suitable computational technique to simulate the truly random path of a neutron in matter based on stochastic nuclear interactions with the nuclei. With regard to fusion reactor applications, there are, in addition, further major advantages of the Monte Carlo method over the deterministic approaches: the ease and flexibility in representing even a complex problem geometry as is typical for tokamak fusion reactors, the possibility of using continuous energy cross-section data thus not being subjected to approximations and limitations when generating and applying group averaged data and, finally, the absence of any numerical convergence problems. At Forschungszentrum Karlsruhe, the Los Alamos National Laboratory Monte Carlo code MCNP is the main computational tools for applications to fusion neutronics problems. In the paper, an overview is given of different task areas with specific examples for blanket and shield design related issues currently being performed in the framework of the European Fusion Technology Programme for ITER, the International Thermonuclear Experimental Reactor, as well as for a Demo-type European tokamak reactor. The focus is on typical design-related neutronic issues such as blanket and shielding performance in terms of tritium breeding, nuclear power generation, radiation penetration through the bulk blanket/shield system, radiation streaming through void gaps, as well as the resulting loads to the superconducting toroidal field coils. For addressing these problems, suitable three-dimensional torus sector models of the different reactors have been developed with the help of the MCNP code. In addition, examples are given of applications to analyses of fusion benchmark experiments which are mainly being performed to validate both the Monte Carlo code and the underlying nuclear cross-section data against fusion relevant integral experiments. The paper finally aims at identifying issues which, in the author's view, require future development work to allow the successful application of the Monte Carlo technique in this and possibly other areas such as advanced means for sensitivity/uncertainty calculations, integration of burn-up calculations and use of CAD generated geometry models in the Monte Carlo calculation.