Over the past decades, exponential integration emerged as a numerical technique that can offer significant computational advantages for integrating large-scale stiff systems of differential equations. In this talk, we will provide an overview of the ways exponential approach can be used to construct new methods and discuss theoretical and practical aspects of design, analysis and implementation of different classes of exponential integrators. We will illustrate performance gains these schemes provide using test problems and several applications in fluid mechanics, plasma physics and computer graphics.