This manuscript reviews recent literatures on synthesis of furfurals (5-hydroxymethylfurfural, furfural, 5-methyl-2-furaldehyde) from various sugars (glucose, fructose, D-galactose, D-arabinose, xylose, L-rhamnose, lactose, cellobiose, sucrose) and furfural conversions into other carbonyl compounds (2,5-diformylfuran, 2,5-furandicarboxylic acid, levulinic acid, succinic acid) using catalytic methodology. Our recent achievements on one-pot synthesis of furfurals using solid acid and base catalysts and selective oxidations of furfurals using heterogeneous catalysts are also included.