As widely recognized, sustainability is a multi- and trans-disciplinary domain potentially able to influence actions, decisions, and behaviors at all the levels of socio-economic organizations. Reflecting upon the pervasive nature of sustainability domain, the paper proposes an overview about the evolutionary path of strategies and approaches for sustainability. Adopting a deductive approach, the main purpose of the paper is to underline in which ways the shifting from a coercive approach to a participatory approach in strategies for sustainability - made possible by the spread of Corporate Social Responsibility practices - has contributed to the emergence of sustainable innovation domain. The concept of Social Engagement in sustainability debate is proposed with the aim to underline that sustainable innovation is effectively possible only in the case in which all the levels of socio-economic organizations are engaged in the debate about sustainability and - as a consequence - they are effectively able to understand and promote the value of an innovation able to combine and satisfy society, economy, and environment needs.