Foams are a type of material of great importance, having an extensive range of applications due to a combination of several characteristics, such as ultra-low density, tunable porous architecture, and outstanding mechanical properties. The production of polymer foams worldwide is dominated by those based on synthetic polymers, which might be biodegradable or non-biodegradable. The latter is a great environmental concern and has become a major waste management problem. Foams derived from renewable resources have aroused the interest of researchers, solid foams made from plant polymers in particular. This review focuses on the development of plant polymer-based solid foams and their applications in the food industry over the last fifteen years, highlighting the relationship between their material and structural properties. The applications of these foams fall mainly into two categories: edible foams and packaging materials. Most plant polymers utilized for edible applications are protein-based, while starch and cellulose are commonly used to produce food packaging materials because of their ready availability and low cost. However, plant polymer-based solid foams exhibit some drawbacks related to their high water absorbency and poor mechanical properties. Most research has concentrated on improving these two physical properties, though few studies give a solid understanding and comprehension of the micro- to macrostructural modifications that would allow for the proper handling and design of foaming processes. There are, therefore, several challenges to be faced, the control of solid foam structural properties being the main one.