Bidirectional transformations bx are a mechanism for maintaining the consistency of two (or more) related sources of information. Researchers from many different areas of computer science including databases (DB), graph transformations (GT), software engineering (SE), and programming languages (PL) are actively investigating the use of bx to solve a diverse set of problems. Although researchers have been actively working on bidirectional transformations in the above mentioned communities for many years already, there has been very little cross-discipline interaction and cooperation so far. The purpose of a first International Meeting on Bidirectional Transformations (GRACE-BX), held in December 2008 near Tokyo, was therefore to bring together international elites, promising young researchers, and leading practitioners to share problems, discuss solutions, and open a dialogue towards understanding the common underpinnings of bx in all these areas. While the GRACE-BX meeting provided a starting point for exchanging ideas in different communities and confirmed our believe that there is a considerable overlap of studied problems and developed solutions in the identified communities, the Dagstuhl Seminar 11031 on ``Bidirectional Transformations'' also aimed at providing a place for working together to define a common vocabulary of terms and desirable properties of bidirectional transformations, develop a suite of benchmarks, solve some challenging problems, and launch joint efforts to form a living bx community of cooperating experts across the identified subdisciplines. This report documents the program and the outcomes of Dagstuhl Seminar 11031 with abstracts of tutorials, working groups, and presentations on specific research topics.