This book highlights designs, implementations and applications of tracking differentiator (TD) algorithms. The real-time differentiation estimation of a given signal is of high importance in control science and engineering. A good differentiator shall have i) robustness against input noises and ii) exactness with a small phase delay. The book has three focuses: Designing practical, accurate and efficient TD based on discrete-time optimal control (DTOC). Presenting full convergence analysis on DTOC-TDs. Implementing the DTOC-TDs in state estimations in power systems and signal processing, as well as feedback control in maglev train. The proposed TD solution and its successful real-life applications shall stimulate wide interests in different areas including power systems, railway transportations and aerospace industry, etc.