Real gases deviate from ideal behavior under high pressure and low temperature because the assumptions of the ideal gas law break down. At high pressure, the volume of gas molecules themselves becomes significant, making the gas less compressible than predicted. At low temperature, weak attractive forces between molecules become noticeable, causing the gas to be more compressible and exert lower pressure. While the ideal gas law is an excellent model for normal conditions, understanding these deviations is crucial for accurate predictions in extreme situations and for explaining phenomena like gas liquefaction.