Abstract: Fractional derivatives and integrals are effective tools to model anomalous diffusions in plasmas, population migration and electrical signal propagation in cardiac tissue. Abel was the first one to use fractional integrals in 1823 to solve the tautochrone problem. Several definitions of fractional derivatives are named after Riemann, Liouville, Caputo, Marchaud and many others. We will give a quick overview on some of these popular definitions and show how different and similar they are. We will also introduce the Mitagg-Leffler functions, which in this context are the fractional analogues of the usual exponential functions. Then we will show a unified approach to fractional derivatives based on the use of semigroups. This will clarify the one-sided nature of fractional derivatives. In the end we will present a (one-sided) Fundamental Theorem of the Fractional Calculus.