This paper presents the goals and some of the results of experiments conducted within the Working Package 10 (Fusion Experimental Programme) of the HiPER Project. These experiments concern the study of the physics connected to 'advanced ignition schemes', i.e. the fast ignition and the shock ignition approaches to inertial fusion. Such schemes are aimed at achieving a higher gain, as compared with the classical approach which is used in NIF, as required for future reactors, and make fusion possible with smaller facilities.In particular, a series of experiments related to fast ignition were performed at the RAL (UK) and LULI (France) Laboratories and studied the propagation of fast electrons (created by a short-pulse ultra-high-intensity beam) in compressed matter, created either by cylindrical implosions or by compression of planar targets by (planar) laser-driven shock waves. A more recent experiment was performed at PALS and investigated the laser–plasma coupling in the 1016 W cm−2 intensity regime of interest for shock ignition.