This book is devoted to a consistent presentation of the recent results obtained by the authors related to controlled systems created based on the Lotka-Volterra competition model, as well as to theoretical and numerical study of the corresponding optimal control problems. These controlled systems describe various modern methods of treating blood cancers, and the optimal control problems stated for such systems, reflect the search for the optimal treatment strategies. The main tool of the theoretical analysis used in this book is the Pontryagin maximum principle - a necessary condition for optimality in optimal control problems. Possible types of the optimal blood cancer treatment - the optimal controls - are obtained as a result of analytical investigations and are confirmed by corresponding numerical calculations. This book can be used as a supplement text in courses of mathematical modeling for upper undergraduate and graduate students. It is our believe that this text will be of interest to all professors teaching such or similar courses as well as for everyone interested in modern optimal control theory and its biomedical applications.