Fractional-order calculus offers novel system modeling possibilities allowing to accurately describe physical phenomena exhibiting memory and/or hereditary properties. The added modeling flexibility is also very useful in control design where robust controllers may be obtained thereby enhancing the performance of control loops. Naturally, conventional controllers, such as the lead/lag compensator and PID controller, have been extended to benefit from noninteger operators. While this is particularly useful in compensating fractional-order dynamics, in general extended tuning freedom of such controllers is acquired, so more performance specifications can be met with better precision. The implementation of fractional-order controllers presents a challenge, however, since mathematically fractional-order operators rely on the entire history of noninteger differentiation/integration and therefore require infinite memory. The solution is to use approximations leveraging the so-called short-memory principle. The presented aspects of fractional-order calculus form the basis of this seminar talk, focusing on the existing issues and the author's contributions. The talk is organized as follows. First, an introduction to the mathematical basis of fractional-order calculus is presented, revealing both the benefits of using noninteger operators and the reasons for the associated difficulties in analysis and computation. Then, an overview of modeling and identification methods for fractional-order dynamical systems is given. In the next part of the talk fractional-order controller tuning methods are discussed. Analog and digital implementations of fractional-order systems and controls are the object of study in the next part. Particular applications of fractional-order controllers are given in the last part of the talk. Finally, conclusions and further research perspectives are outlined.