Machine learning methods have recently seen a rapid development, both in terms of variety of model architectures (feedforward, recurrent, convolutional neural networks, transformers), training methods
(gradient descent, adversarial and property-based training) and sheer sizes of models. Thanks to these developments, machine learning is being incorporated in an ever growing number of applications, ranging from traditional computer vision applications, to more recent domains such as conversational agents and scientific computing. However, neural networks, new and old equally, suffer from a range of safety and security problems, such as vulnerability to adversarial attacks, data poisoning, catastrophic forgetting. Blindly adapting neural networks to safety critical domains may lead to a whole range of issues that machine-learning-free applications were not prone to. This problem led to the development of neural network verification, a hybrid field that merges formal methods and security with machine learning methods, with the purpose of developing robust tools and methods to guarantee safe neural network operation. In this talk, I will overview some of the pitfalls and challenges in adapting neural networks to different domains, and discuss their common symptoms and underlying technical reasons. I will survey the existing methods to safeguard neural networks or applications incorporating neural networks; focusing in particular on the available methods and tools of neural network verification.