An outdoor structure, in particular a modular outdoor kitchen, comprising: a plurality of vertically extending walls joined together to form a standing structure surrounding an interior volume; each of the walls comprising: (a) a plurality of structural polymer panels with a thickness of at least 2.54 cm (1 inch), opposite top and bottom edges, and opposite side edges, each structural polymer panel having a foam panel, the structural polymer panel having a panel face and perimeter edges surrounding the panel face; (b) a plurality of veneer members each having a front surface, a back surface, and an outer periphery surrounding the front and back surfaces, and a thickness between the front and back surfaces of not greater than 10.16 cm (4 inches); and (c) structural bond adhesive directly adhering the veneer members onto the structural polymer panels to the panel face along the back surfaces of the veneer members and also adhering to adjacent veneer members along the outer periphery of the veneer members; and wherein the structural polymer panels are fitted together along the side edges and stood along bottom edges to form a frameless standing structure surrounding an interior volume, wherein the standing structure has a compressive strength of at least 172 kPa (25 psi), and wherein the structural polymer panel and veneer members of the wall bears at least 90% of a load on the standing structure. a plurality of vertically extending walls joined together to form a standing structure surrounding an interior volume; each of the walls comprising: (a) a plurality of structural polymer panels with a thickness of at least 2.54 cm (1 inch), opposite top and bottom edges, and opposite side edges, each structural polymer panel having a foam panel, the structural polymer panel having a panel face and perimeter edges surrounding the panel face; (b) a plurality of veneer members each having a front surface, a back surface, and an outer periphery surrounding the front and back surfaces, and a thickness between the front and back surfaces of not greater than 10.16 cm (4 inches); and (c) structural bond adhesive directly adhering the veneer members onto the structural polymer panels to the panel face along the back surfaces of the veneer members and also adhering to adjacent veneer members along the outer periphery of the veneer members; and (a) a plurality of structural polymer panels with a thickness of at least 2.54 cm (1 inch), opposite top and bottom edges, and opposite side edges, each structural polymer panel having a foam panel, the structural polymer panel having a panel face and perimeter edges surrounding the panel face; (b) a plurality of veneer members each having a front surface, a back surface, and an outer periphery surrounding the front and back surfaces, and a thickness between the front and back surfaces of not greater than 10.16 cm (4 inches); and (c) structural bond adhesive directly adhering the veneer members onto the structural polymer panels to the panel face along the back surfaces of the veneer members and also adhering to adjacent veneer members along the outer periphery of the veneer members; and wherein the structural polymer panels are fitted together along the side edges and stood along bottom edges to form a frameless standing structure surrounding an interior volume, wherein the standing structure has a compressive strength of at least 172 kPa (25 psi), and wherein the structural polymer panel and veneer members of the wall bears at least 90% of a load on the standing structure.