The construction industry suffers from unsustainability and contributes more than any other industrial sector to carbon emissions that lead to global warming. Increasing economic and environmental concerns related to conventional energy- and CO2-intensive building materials have propelled the rapid and sustained expansion of research in the area of plant-based inorganic mineral binder-bonded materials for the construction industry. The resulting composites can be qualified as eco-responsible, sustainable, and efficient multifunctional building materials. So far, most of these research efforts have not received as much attention as materials based on ordinary Portland cement (OPC). To address this gap, this review focuses on mineral binder-based lignocellulosic composites made from non-conventional inorganic mineral binders/ cements with low embodied energy and low carbon footprint, namely hydrated lime-based binders, magnesium-based cement, alkali-activated cement, and geopolymers, as sustainable alternatives to OPC-bonded lignocellulosic composites (state-of-the-art). The emphasis here is on the application potentials, the influence of production parameters on the material properties/ performance, and recent advancement in this field. Finally, a prediction is provided of future trends for these non-conventional mineral binder-bonded lignocellulosic composites.