Increasing the production of energy in line with industry development, transportation, and life quality improvement is an interesting topic needs to be addressed. Energy policymakers and researchers have aimed at energy management, particularly by improving energy systems performance. This review paper explains the rising interest of thermoelectric technology and applications. Nowadays, thermoelectric technology such as thermoelectric generators (TEGs) and thermoelectric cooling systems (TECs) provide heat loss recovery of thermodynamic units for power production of remote areas. Unlimited solar energy can also be employed for thermoelectric power production. This paper describes the principles of thermoelectricity and presents an explanation of current and upcoming materials. Developed models and various performed optimization of thermoelectric applications by using non-equilibrium thermodynamics and finite time thermodynamics are discussed as well. Additionally, a number of topical applications and energy resources are introduced. The main goal of this study is to give a clear overview of thermoelectric technology and applications. •Explains the rising interest of thermoelectric technology and applications.•Describes thermoelectricity principles and current and upcoming materials.•Developed models and various performed optimization are discussed.•Includes non-equilibrium thermodynamics and finite time thermodynamics.•A number of topical applications and energy resources are introduced.