Present thesis is devoted to the research of fractional-order calculus in the context of modeling, identification and control of dynamic systems. The first part of the thesis introduces the reader to the theoretical concepts behind fractional-order calculus and its applications in system theory, system identification and control. In the second part the FOMCON (“Fractional-order Modeling and Control”) toolbox for MATLAB, developed by the author, is presented and a detailed user manual for it is provided with illustrative examples. All major calculations and simulations performed in this thesis are done in the MATLAB/Simulink environment. Additionally, some examples are performed using Maxima and Scilab computer algebra systems. It is assumed that the reader has previous knowledge in the field of system theory.