Demonstrating ignition and net energy gain in the near future on MJ-class laser facilities will be a major step towards determining the feasibility of Inertial Fusion Energy (IFE), in Europe as in the United States. The current status of the French Laser MégaJoule (LMJ) programme, from the laser facility construction to the indirectly driven central ignition target design, is presented, as well as validating experimental campaigns, conducted, as part of this programme, on various laser facilities. However, the viability of the IFE approach strongly depends on our ability to address the salient questions related to efficiency of the target design and laser driver performances. In the overall framework of the European HiPER project, two alternative schemes both relying on decoupling target compression and fuel heating—fast ignition (FI) and shock ignition (SI)—are currently considered. After a brief presentation of the HiPER project's objectives, FI and SI target designs are discussed. Theoretical analysis and 2D simulations will help to understand the unresolved key issues of the two schemes. Finally, the on-going European experimental effort to demonstrate their viability on currently operated laser facilities is described.