When it was first introduced, the concept of sustainability in the forestry sector had a narrow focus on sustainable wood production. Since then, this concept has evolved and it now considers now the three sustainability dimensions (economic, environmental and social) of the whole forest wood supply chain. The main objective of this study is then to review assessment and optimization studies that consider the forest wood supply chain and at least one of the sustainability dimensions. To accomplish this goal, a total number of 188 papers, published in English-speaking peer-reviewed journals from 1995 to 2017, were reviewed. These papers have been classified according to the sustainability dimensions explored, the stakeholder’s involvement, the modeling approaches applied, the supply chain decision levels treated, the uncertainty inclusion, and case study analyzed. Most of the studies reviewed (84.6%) considered only two sustainability dimensions: economic (31.9%), environmental (13.8%), or a combination of both (38.8%). The first study including the three sustainability dimensions was published in 2005. Most of the studies reviewed (64.9%) focus on the bioenergy industry in Europe and North America, due to the growing interest in using biomass to substitute fossil fuels in energy production. The final part of the paper presents the identified specific features of sustainable forest wood supply chains and discusses a future research agenda in the area.