The need for mechatronic devices that are lightweight, less cumbersome and able to produce small, quick and precise movements or forces is ever increasing in many fields of engineering. Many recent design solutions are based on electrically, magnetically or thermally activated materials, often referred to as smart materials. This tutorial paper overviews the main properties and the resulting applications of two recently discovered smart materials, magnetic shape memory alloys (MSMAs) and electroactive polymers (EAPs), which have complementary characteristics and seem suitable to overcome some of the inherent limitations of other materials widely used in industrial applications, such as piezoelectric ceramics. As many other smart materials, MSMAs and EAPs exhibit nonlinear, hysteretic and time-varying behaviors, and therefore this tutorial discusses the main ways to model and effectively compensate these critical issues with advanced control strategies.