Community Wireless Networks (CWNs) are community-driven solutions that provide ubiquitous and affordable or free wireless Internet access in order to improve the well-being of the community. The escalation of this innovation and diversity of its business models have raised many concerns about the viability and sustainability of such a young innovation. Specifically, CWNs can be implemented using diverse business models that vary with respect to different social sittings, and adopting the proper business model is the key to success for these nonprofit projects. This paper proposes a typology through which we conceptualize and classify these models and discuss their advantages and disadvantages considering their social sittings. We have identified the value offering, financial aspects, business partners, infrastructure management, and target customers of these models. This work would help practitioners to choose the most suitable business model for their community and researchers to investigate the social and economic implications of this innovation.