High-energy charged particles in the van Allen radiation belts and in solar energetic particle events can damage satellites on orbit leading to malfunctions and loss of satellite service. Here we describe some recent results from the SPACECAST project on modelling and forecasting the radiation belts, and modelling solar energetic particle events. We describe the SPACECAST forecasting system that uses physical models that include wave-particle interactions to forecast the electron radiation belts up to 3 h ahead. We show that the forecasts were able to reproduce the >2 MeV electron flux at GOES 13 during the moderate storm of 7-8 October 2012, and the period following a fast solar wind stream on 25-26 October 2012 to within a factor of 5 or so. At lower energies of 10- a few 100 keV we show that the electron flux at geostationary orbit depends sensitively on the high-energy tail of the source distribution near 10 RE on the nightside of the Earth, and that the source is best represented by a kappa distribution. We present a new model of whistler mode chorus determined from multiple satellite measurements which shows that the effects of wave-particle interactions beyond geostationary orbit are likely to be very significant. We also present radial diffusion coefficients calculated from satellite data at geostationary orbit which vary with Kp by over four orders of magnitude. We describe a new automated method to determine the position at the shock that is magnetically connected to the Earth for modelling solar energetic particle events and which takes into account entropy, and predict the form of the mean free path in the foreshock, and particle injection efficiency at the shock from analytical theory which can be tested in simulations.