Detecting anomalies in telemetry data captured on-board a spacecraft is a critical aspect of its safe operation, and it allows us to effectively and timely respond to failures and hazards. There exist three main types of anomalies that should be considered for such complex missions. In point anomalies, telemetry values fall outside the nominal operational range. The collective anomalies refer to the overall sequences of consecutive telemetry values that are anomalous (a single data point does not necessarily manifest an anomaly), whereas in contextual anomalies, the single values are anomalous within their local neighborhood. There have been various approaches for automating the process of detecting anomalies from telemetry data. The basic yet widely exploited algorithms include the out-of-limit techniques that are built upon the assumption that we have the prior expert knowledge allowing us to exploit a rule-based approach for detecting unexpected events. There are machine learning algorithms for this task, but they are commonly heavily parameterized and require large amounts of ground-truth (manually delineated) data, ideally with captured anomalies. Since acquiring such data is infeasible in practice, unsupervised techniques have attracted the research attention, as they do not require having large training samples to train well-generalizing models. In this paper, we not only review the current state of the art in anomaly detection from telemetry data, but also present our algorithm for this task – being developed as a part of our Antelope on-board computer with predictive maintenance capabilities – which exploits recurrent neural networks (we are currently utilizing long short-term memory networks) to model the expected telemetry signal. Such models can be trained from a set of the simulated nominal telemetry signals (e.g., using the software or hardware-in-the-loop simulators), or from a set of real-life telemetry presenting the nominal operation. Importantly, we can learn from the correct examples that do not contain anomalous events – it allows us to abstract from the type of anomalies that we want to target. Once the expected signal is elaborated, it is confronted with the actual one, and the obtained error triggers the alert showing that the anomaly has appeared. We additionally show how to thoroughly verify the anomaly detection techniques in a quantitative way, and what kind of metrics comprehensively reflect the underlying abilities of such deep learning techniques. Finally, we will present our visualization tools that help us better understand the advantages and shortcomings of various anomaly detection methods and will discuss our experiments performed over benchmark one-dimensional signal, and real-life telemetry captured on-board the European Space Agency’s OPS-SAT satellite. Since the Antelope will be exploited on-board a satellite, our resource-frugal models will ultimately help us respond to the events quicker and could be used to reduce the amount of data to transfer back to Earth through annotating the most important parts of the signal that enable further analysis and interpretation.