Virtually any software running on a computer has been processed by a compiler or a compiler-like tool. Because compilers are such a crucial piece of infrastructure for building software, their correctness is of paramount importance. To validate and increase the correctness of compilers, significant research efforts have been devoted to testing compilers. This survey article provides a comprehensive summary of the current state-of-the-art of research on compiler testing. The survey covers different aspects of the compiler testing problem, including how to construct test programs, what test oracles to use for determining whether a compiler behaves correctly, how to execute compiler tests efficiently, and how to help compiler developers take action on bugs discovered by compiler testing. Moreover, we survey work that empirically studies the strengths and weaknesses of current compiler testing research and practice. Based on the discussion of existing work, we outline several open challenges that remain to be addressed in future work.