This book constitutes the refereed proceedings of the 7th International Conference on Theory and Applications of Models of Computation, TAMC 2010, held in Prague, Czech Republic, in June 2010. The 35 revised full papers presented together with 5 contributions of special sessions as well as 2 plenary talks were carefully reviewed and selected from 76 submissions. The papers address the three main themes of the conference which were computability, complexity, and algorithms and present current research in these fields with aspects to theoretical computer science, algorithmic mathematics, and applications to the physical sciences.