Crowd-Shipping (CS) solutions have been gaining popularity in industry and academia. Despite numerous CS platforms having been introduced in the real world, only a limited number of them have managed to remain viable. Academics have explored many challenges facing CS platforms and recommended appropriate solution measures. While the growing literature sporadically indicates "economic", "environmental" or even "societal" benefits of CS initiatives, there is a lack of systematic and conclusive understanding of CS initiatives from these essential "sustainability perspectives". Considering that sustainability and societal impacts of such new and emerging initiatives are key factors in gaining public policy support and potential government investments and involvements, as critical success factors for the uptake, growth and continuity of these initiatives, this paper aims to present a review of this topic in light of sustainability considerations. A content-based framework grounded on the Triple Bottom Line (TBL) approach is adopted in this review and papers are reviewed, classified, synthesised, and analysed to reveal dominant research trends, challenges, potential and gaps. Furthermore, our analysis of the economic and behavioural considerations of CS actors reveals important insights into how various pricing strategies can be adopted to regulate supply and demand for operational continuity. Finally, using an intersectional sustainability approach, future research directions are also recommended to fill the gaps and improve the practical relevance of CS.