  In recent years, software systems powered by deep learning (DL) techniques
have significantly facilitated people's lives in many aspects. As the backbone
of these DL systems, various DL libraries undertake the underlying optimization
and computation. However, like traditional software, DL libraries are not
immune to bugs, which can pose serious threats to users' personal property and
safety. Studying the characteristics of DL libraries, their associated bugs,
and the corresponding testing methods is crucial for enhancing the security of
DL systems and advancing the widespread application of DL technology. This
paper provides an overview of the testing research related to various DL
libraries, discusses the strengths and weaknesses of existing methods, and
provides guidance and reference for the application of the DL library. This
paper first introduces the workflow of DL underlying libraries and the
characteristics of three kinds of DL libraries involved, namely DL framework,
DL compiler, and DL hardware library. It then provides definitions for DL
underlying library bugs and testing. Additionally, this paper summarizes the
existing testing methods and tools tailored to these DL libraries separately
and analyzes their effectiveness and limitations. It also discusses the
existing challenges of DL library testing and outlines potential directions for
future research.
