There is a strong need to develop and implement appropriate alternatives to replace formaldehyde-based adhesive systems, such as phenol–formaldehyde, in the industry of wood-based panels (WBPs). This is due to the toxicity and volatility of formaldehyde and restrictions on its use associated with some formaldehyde-based adhesives. Additionally, the current pressure to reduce the dependence on polymeric materials, including adhesives, from petrochemical-based sources has led to increased interest in bio-based adhesives, which, in some cases, already provide acceptable properties to the end-product. Among the potential raw materials for good-quality, renewable-based adhesive formulations, this paper highlights tannins, lignin, and protein sources. However, regarding renewable sources, specific features must be considered, such as their lower reactivity than certain petrochemical-based sources and, therefore, higher production costs, resource availability issues, and the need for toxicological investigations on alternative systems, to compare them to conventional systems. As a result, further research is highly encouraged to develop viable formaldehyde-free adhesive systems based on renewable sources, either at the technical or economical level. Moreover, herein, we also showcase the present market of WBPs, highlighting the obstacles that the alternative and new bio-based adhesives must overcome.