In the current jurisprudential debate, the issue of conflicts of rights is a widely debated one. The present essay aims at clarifying the main aspects of this ongoing debate, along the following lines: firstly, an historical account of the problem of balancing conflicting rights will be given, with an eye both to the American recent experience and to the Italian one. Secondly, it will be discussed whether and under what circumstances rights can conflict. Thirdly, after having acknowledged that conflicts of rights are in fact unavoidable, it will be necessary to examine the main technique of solving those conflicts: namely, the "weighing and balancing" technique. The main suggestion that is intended to follow from the whole discussion is that the technique of balancing involves for sure a certain (sometimes, considerable) degree of interpretive discretion, but nonetheless - at least under some circumstances -- it is not necessarily incompatible with legal certainty and predictability of legal decisions.