The penetration of renewable energies is increasing in power systems all over the world. The volatility and intermittency of renewable energies pose real challenges to energy systems. To overcome the problem, demand-side flexibility is a practical solution in all demand sectors, including residential, commercial, agricultural, and industrial sectors. This paper provides a comprehensive review of industrial demand response opportunities in energy-intensive industries. Flexibility potentials are discussed from (1) viewpoints of power flexibility for cement manufacturing and aluminum smelting plants (2) viewpoints of joint power-heat flexibility for oil refinery industries. The flexibility potentials of industrial processes are classified based on their compatibility with time responses on long, mid, and short advance notices of different electricity market floors and ancillary service markets. Challenges and opportunities of industrial demand management are classified from viewpoints of power systems and industry owners. Software tools and solution methodologies of industrial energy models are surveyed for energy researchers. The studies show that cement manufacturing plants have great potentials in providing peak-shaving and valley-filling in crushers and cement mills with up to 10% and 16.9% reduction in energy consumption cost and power consumption, respectively. The aluminum smelting plants can provide up to 34.2% and 20.70% reduction in energy consumption cost and power consumption by turning down/off the variable voltage smelting pots.