In the universe's earliest moments, particles existed in an unimaginably hot plasma, whose behavior was governed by deeply complex webs of interaction between individual particles. Today, researchers can recreate these exotic conditions through high-energy collisions between heavy ions, whose products can tell us much about how hot, strongly-interacting matter behaves. Yet without extensive, highly coordinated collaborations between researchers across many different backgrounds, studies like this simply wouldn't be possible. This Topical Issue of EPJ A draws together a large collection of papers inspired by the theory of hot matter and relativistic heavy-ion collisions (THOR) European Cooperation in Science and Technology (COST) Action. Running between November 2016 and April 2021, THOR has provided a way for over 300 researchers involved in heavy-ion collision analysis to freely exchange their ideas, leading to exciting new advances in the wider field of particle physics.