A cooking grate assembly (2, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 730, 740, 760, 770, 800, 850, 900, 950) comprising: a lower structure comprising a side-by-side series of parallel, longitudinally extending solid sections (8, 102, 152, 202, 402, 452, 502) having substantially no openings therethrough; a series of parallel, longitudinally extending open sections (10, 12) provided in said lower structure, said open sections (10, 12) being located between said solid sections (8, 102, 152, 202, 402, 452, 502), each of said open sections (10, 12) having an open area lateral width; and an upper structure comprising a side-by-side series of parallel, spaced apart, longitudinally extending food support ribs (14, 732, 742, 764, 774), each having a hollow interior and a longitudinally extending bottom opening, said bottom opening having a lateral width that is not less than said open area lateral width of said open sections (10, 12) of said lower structure, and each of said food support ribs (14, 732, 742, 764, 774) having one or more gas outlet openings (22, 40, 552, 772) characterized by said upper structure having gaps between said food support ribs (14, 732, 742, 764, 774), wherein said upper structure being removably positionable over said lower structure such that said food support ribs (14, 732, 742, 764, 774) are positioned over and substantially parallel to said open sections (10, 12) of said lower structure so that, as viewed from above said cooking grate assembly (2, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 730, 740, 760, 770, 800, 850, 900, 950), said food support ribs (14, 732, 742, 764, 774) substantially entirely cover said open sections (10, 12) of said lower structure and said solid sections (8, 102, 152, 202, 402, 452, 502) are positioned in said gaps between said food support ribs (14, 732, 742, 764, 774); and when said upper structure is positioned over said lower structure, said open sections (10, 12) of said lower structure are located within, at, or below said bottom openings of said food support ribs (14, 732, 742, 764, 774) in a manner such that combustion gases flowing upwardly through said open sections (10, 12) of said lower structure will continuously flow into said hollow interiors of said food support ribs (14, 732, 742, 764) and out of said gas outlet openings (22, 40, 552, 772) of said food support ribs (14, 732, 742, 764) so that said combustion gases do not remain stagnant in said hollow interiors of said food support ribs (14, 732, 742, 764). a lower structure comprising a side-by-side series of parallel, longitudinally extending solid sections (8, 102, 152, 202, 402, 452, 502) having substantially no openings therethrough; a series of parallel, longitudinally extending open sections (10, 12) provided in said lower structure, said open sections (10, 12) being located between said solid sections (8, 102, 152, 202, 402, 452, 502), each of said open sections (10, 12) having an open area lateral width; and an upper structure comprising a side-by-side series of parallel, spaced apart, longitudinally extending food support ribs (14, 732, 742, 764, 774), each having a hollow interior and a longitudinally extending bottom opening, said bottom opening having a lateral width that is not less than said open area lateral width of said open sections (10, 12) of said lower structure, and each of said food support ribs (14, 732, 742, 764, 774) having one or more gas outlet openings (22, 40, 552, 772) characterized by said upper structure having gaps between said food support ribs (14, 732, 742, 764, 774), wherein said upper structure being removably positionable over said lower structure such that said food support ribs (14, 732, 742, 764, 774) are positioned over and substantially parallel to said open sections (10, 12) of said lower structure so that, as viewed from above said cooking grate assembly (2, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 730, 740, 760, 770, 800, 850, 900, 950), said food support ribs (14, 732, 742, 764, 774) substantially entirely cover said open sections (10, 12) of said lower structure and said solid sections (8, 102, 152, 202, 402, 452, 502) are positioned in said gaps between said food support ribs (14, 732, 742, 764, 774); and when said upper structure is positioned over said lower structure, said open sections (10, 12) of said lower structure are located within, at, or below said bottom openings of said food support ribs (14, 732, 742, 764, 774) in a manner such that combustion gases flowing upwardly through said open sections (10, 12) of said lower structure will continuously flow into said hollow interiors of said food support ribs (14, 732, 742, 764) and out of said gas outlet openings (22, 40, 552, 772) of said food support ribs (14, 732, 742, 764) so that said combustion gases do not remain stagnant in said hollow interiors of said food support ribs (14, 732, 742, 764).