This book constitutes the refereed proceedings of the 13th International Conference on Reversible Computation, RC 2021, which was held online during July 7-8, 2021. The 11 papers included in this book were carefully reviewed and selected from 21 submissions.

Invited Talks.- How Can We Construct Reversible Turing Machines in a Very Simple Reversible Cellular Automaton.- Variational Quantum Eigensolver and Its Applications.- Programming and Programming Languages.- Reversible Functional Array Programming.- Compiling Janus to RSSA.- Causal-Consistent Debugging of Distributed Erlang Programs.- Towards a Unified Language Architecture for Reversible Object-Oriented Programming.- Reversible Concurrent Computation.- Towards a truly concurrent semantics for reversible CCS.- Forward-Reverse Observational Equivalences in CCSK.- Explicit Identifiers and Contexts in Reversible Concurrent Calculus.- Reversibility and predictions.- Theory and Foundations.- A Tangled Web of 12 Lens Laws.- Splitting recursion schemes into reversible and classical interacting threads.- Reversibility of Executable Interval Temporal Logic Specifications.- Circuit Synthesis.- Efficient Construction of Functional Representations for QuantumAlgorithms.- Finding Optimal Implementations of Non-native CNOT Gates using SAT.- Fast Swapping in a Quantum Multiplier Modelled as a Queuing Network.- OR-Toffoli and OR-Peres Reversible Gates.