"Church's Thesis" (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of a effectively computable function defined in natural numbers with the notion of a recursive function. Despite of the many efforts of prominent scientists, "Church's Thesis" has never been falsified. There exists a vast literature concerning the thesis. The aim of the book is to provide one volume summary of the state of research on "Church's Thesis". These include the following: different formulations of CT; CT and intuitionism; CT and intentional mathematics; CT and physics; the epistemic status of CT; CT and philosophy of mind; provability of CT; and CT and functional programming.