The aim of this introductory paper is twofold. First, we seek to illustrate which are the difficulties into which one runs when one attempts to give a precise definition of what bioart is. Our hypothesis is that every attempt at such definition runs into a paradox. Indeed, if on the one hand, every definition seems inevitably reductionist, unjustly omitting one or more elements, on the other hand, defining and constraining the study area is a necessary preliminary step to understand the artistic phenomenon known as bioart. In the second part of our paper, attention will be focused on the ethical issues that bioart confront us with. These issues are all the more relevant, given the fact that bioartists often make use of biotechnologies to manipulate living organisms for artistic purposes.