Diversifying in a responsible way is a challenge that many firms face today. In this survey we posit whether firms should diversify and whether it is a way to create value, since the motives leading to diversification are not always addressed to satisfying all stakeholders, and as a consequence the outcome may be different from the one expected. Our aim is to smooth the way for managers, shareholders, professionals and decision-makers in general by offering an exhaustive and rigorous description of the lessons provided by the literature, analyzing the reasons for diversifying or not, describing the costs and benefits of the process and analyzing the discount on firm value.