Thirty thousand to two hundred thousand years ago, Neanderthals roamed the land of much of Europe and Western Asia. First discovered in a German limestone quarry in 1856, this curious species was distinct from us, and yet also not so different. Similar to modern humans (Homo sapiens sapiens), the Neanderthals (Homo neanderthalensis) used tools, made and wore jewelry, played musical instruments, painted in caves, and most likely developed a language of sorts. Moreover, many people today possess Neanderthal DNA in their genomes, raising a variety of questions as to the identity of these mysterious beings. For instance, what is the nature of the evolutionary relationship between modern humans and Neanderthals? Given that Homo sapiens and Neanderthals co-inhabited the Earth, did they merely live side-by-side, or did they interbreed and interact? What are the implications of possessing Neanderthal DNA? Does this ancient genetic material affect medical outcomes? In particular, in light of the rise of COVID-19, can the presence of Neanderthal DNA affect outcomes for those hospitalized for COVID-19 infections? Finally, why did the Neanderthals disappear from the Earth and what factors led to their extinction? These questions and more will be explored in Neanderthals: Exploring our Genetic Past and Present, a collection of essays authored by students of Canadian universities.