Several classes of biological molecules that transform chemical energy into mechanical work are known as motor proteins or molecular motors. These nanometer-sized machines operate in noisy stochastic isothermal environment, strongly supporting fundamental cellular processes such as transfer of genetic information, transport, organization and functioning. In last two decades motor proteins have become a subject of intense research efforts that were aimed to uncover fundamental principles and mechanisms of molecular motors dynamics. In this review, we critically discuss a recent progress in experimental and theoretical studies on motor proteins. Our focus is on analyzing fundamental concepts and ideas that have been utilized for explaining non-equilibrium nature and mechanisms of molecular motors.