Large scale numerical models of systems evolving over a wide range of temporal and spatial scales are routinely encountered in a variety of fields from fluid mechanics and plasma physics to weather prediction and chemical engineering. Many of such, so-called stiff, systems present a computational challenge and fuel continuous need to improve the fidelity, robustness and efficiency of numerical time integrators. Over the past decades, exponential integration emerged as a numerical technique that carries significant computational savings. In this talk we will explain advantages exponential methods offer and discuss theoretical and practical aspects of designing and implementing different classes of efficient exponential integrators. We will illustrate performance gains these schemes provide using test problems and examples from several applications in plasma physics and computer graphics.