Over the past several decades exponential integration has become a more prominent topic in numerical analysis and scientific computing. It is still, however, a new-kid-on-the-block compared to the extensively studied and used explicit and implicit temporal integrators. Thus, no broad recognition exists in the scientific community on how to answer questions like when one should use an exponential method, what kind of exponential schemes are appropriate for specific problems or what an efficient implementation of an exponential integrator looks like. In this talk, we will attempt to address some of these issues and present considerations that can guide the construction, analysis and application of exponential methods. We will discuss how different classes of exponential integrators can be derived and outline the intricacies of their implementation particularly for high performance computing platforms. A novel approach to derivation of exponential schemes using stiffness-resilient framework will be described and performance of the novel methods will be demonstrated on a suite of numerical tests. We will show how taking into account the structure of the application of interest can lead to construction of exponential schemes particularly efficient for this problem. Examples from fields such as plasma physics, numerical weather prediction and computer graphics will be used.