This paper shortly summarises the experimental results obtained since 2011 by a large European academic consortium for the scientific conceptualisation, the definition of the technical requirements, the generation of experimental data, and the validation of a numerical code, for the Pulsating Heat Pipes (PHP) experiment on the International Space Station (ISS). The PHP is a passive, wickless thermal device, whereby a two-phase fluid, forming liquid plugs and vapour slugs, moves with a pulsating or circulating motion inside a meandering tube or channel. The PHP may have a very broad range of geometries (flat, tubular, 3D structured), it can dissipate heat from large areas, and it can be suitable for high power applications with low/medium heat fluxes. PHP functioning is based on the capillary effect, which provides the existence of liquid plugs completely filling the channel cross-section, in a way that any expansion or contraction of the vapour slugs will naturally generate a movement of the fluid along the channel axis. For this, it is important that the channel has a cross-section size below a given threshold, which depends on the liquid surface tension and (for a static fluid) on the gravity acceleration. In space, when only residual accelerations are acting, such a static size threshold is virtually infinite, while a finite dynamic threshold exists even in the absence of gravity. The concept of a "Space PHP" was originally developed in 2014 by the team, and from then 17 Parabolic Flight Campaigns (PFC) and 3 Sounding Rocket (SR) experiments have been carried out to generate the data for the preparation of an experiment targeting a Low Earth Orbit (LEO) mission. Both a tubular and a flat plate PHP have been successfully tested in reduced gravity and on ground, by using different combinations of fluids and building materials. The need for having an experiment on a LEO environment is mainly because, during a PFC, only 22sec of reduced gravity are possible, which is a period below the characteristic time for reaching a steady state condition for almost all of the tested devices. Instead, a steady state was reached using the SR campaigns: in this case however, only one experimental condition was achievable, and long-duration data of the PHP performance still remains beyond reach. Several measurement methodologies have been used to characterise the Space PHP, like infrared analysis, high-speed camera visualisation techniques, with data processed with different techniques, from wavelets to inverse heat transfer problem solution. The results clearly showed that PHPs are very interesting for space applications due to their simplicity of construction, the capacity to transfer heat up to several hundred watts, a high power/weight ratio, their geometrical adaptability, and, in particular, the Space PHP will be a breakthrough technology for space thermal management.