Polymers have both physical and mechanical properties. Some key physical properties include solubility in solvents, how they are affected by heat, and their ability to allow diffusion of molecules. Their mechanical properties include toughness, strength, and elasticity. Polymers dissolve in solvents and swell in size, while melting and decomposing at certain temperatures above room temperature. Their strength depends on factors like chain length and cross-linking, while their elasticity comes from their molecular structure.