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Machine learning has become prevalent across a wide variety of applications. Unfortunately, machine learning has also shown to be susceptible to deception, leading to errors, and even fatal failures. This circumstance calls into question the widespread use of machine learning, especially in safety-critical applications, unless we are able to assure its correctness and trustworthiness properties. Software verification and testing are established technique for assuring such properties, for example by detecting errors. However, software testing challenges for machine learning are vast and profuse - yet critical to address. This summary talk discusses the current state-of-the-art of software testing for machine learning. More specifically, it discusses six key challenge areas for software testing of machine learning systems, examines current approaches to these challenges and highlights their limitations. The paper provides a research agenda with elaborated directions for making progress toward advancing the state-of-the-art on testing of machine learning.