Nowadays, deep neural networks (DNNs) play a crucial role in decision-making processes across various applications, such as self-driving vehicles, medical diagnostics, and industrial automation. The safety-critical nature of these applications has motivated the research on developing automated techniques to verify essential properties (e.g., robustness and fairness) in DNNs. However, although the literature on static verification is well established, there is more to be done on DNNs runtime monitoring. This paper compares state-of-the-art approaches for recognizing anomalies during DNN execution, including out-of-distribution (OoD) detection and runtime verification. In particular, we examine techniques leveraging the softmax layer output for OoD runtime monitoring methods, alongside methods that exploit the network’s internal neuron activation patterns. Our analysis highlights the importance of DNN monitoring and summarizes the challenges and opportunities in this field.