What we would like to know about extreme horizontal branch stars in globular clusters

In this contribution, we explore some open questions about Extreme Horizontal Branch (EHB) stars in globular clusters. In particular, we present the current status of the search for rapid pulsators, He-depleted stars, and close binaries, three kind of objects very common among field EHB stars, but which first surveys failed to detect in clusters. We also analyze how the lack of cluster EHB binaries can reconcile with theoretical expectations. We give special attention to the first close EHB binary discovered in a globular cluster, whose characteristics point to a very rare or even unique object. Finally, we analyze some recent puzzling results about spectroscopically derived masses, that could point to the presence of two distinct families of EHB’s in clusters. For all these topics, we present the recent advancement in knowledge, the results requiring more investigation, and what has still to be done to fix the unsolved problems, showing the main points of our studies, the aims of our works, and what we expect to obtain from them.