Defects are usually seen as imperfections in materials that could significantly degrade their performance. However, at the nanoscale, defects could be extremely useful since they could be exploited to generate novel, innovative and useful materials and devices. Graphene and graphene nanoribbons are no exception. This review therefore tries to categorize defects, emphasize their importance, introduce the common routes to study and identify them and to propose new ways to construct novel devices based on 'defective' graphene-like materials. In particular, we will discuss defects in graphene-like systems including (a) structural (sp(2)-like) defects, (b) topological (sp(2)-like) defects, (c) doping or functionalization (sp(2)- and sp(3)-like) defects and (d) vacancies/edge type defects (non-sp(2)-like). It will be demonstrated that defects play a key role in graphene physicochemical properties and could even be critical to generate biocompatible materials. There are numerous challenges in this emerging field, and we intend to provide a stimulating account which could trigger new science and technological developments based on defective graphene-like materials that could be introduced into other atomic layered materials, such as BN, MoS(2) and WS(2), not discussed in this review.