The 229-thorium isomer: doorway to the road from the atomic clock to the nuclear clock

The elusive 'thorium isomer', i.e. the isomeric first excited state of Th-229, has puzzled the nuclear and fundamental physics communities for more than 40 years. With an exceptionally low excitation energy and a long lifetime it represents the only known candidate so far for an ultra-precise nuclear frequency standard ('nuclear clock'), potentially able to outperform even today's best timekeepers based on atomic shell transitions, and promising a variety of intriguing applications. This tutorial reviews the development of our current knowledge on this exotic nuclear state, from the first indirect evidence in the 1970s, to the recent breakthrough results that pave the way towards the realization of a nuclear clock and its applications in practical fields (satellite based navigational systems and chronometric geodesy) as well as fundamental physics beyond the standard model (the search for topological dark matter and temporal variations of fundamental constants).