The detection and measurement of transient episodes of crustal deformation from global InSAR datasets are crucial for a wide range of solid earth and natural hazard applications. But the large volumes of unlabelled data captured by satellites preclude manual systematic analysis, and the small signal-to-noise ratio makes the task difficult. In this thesis, I present a state-of-the-art, unsupervised and event-agnostic deep-learning based approach for the automatic identification of transient deformation events in noisy time-series of unwrapped InSAR images. I adopt an anomaly detection framework that learns the ‘normal’ spatio-temporal pattern of noise in the data, and which therefore identifies any transient deformation phenomena that deviate from this pattern as ‘anomalies’. The deep-learning model is built around a bespoke autoencoder that includes convolutional and LSTM layers, as well as a neural network which acts as a bridge between the encoder and decoder. I train our model on real InSAR data from northern Turkey and find it has an overall accuracy and true positive rate of around 85% when trying to detect synthetic deformation signals of length-scale > 350 m and magnitude > 4 cm. Furthermore, I also show the method can detect (1) a real Mw 5.7 earthquake in InSAR data from an entirely different region- SW Turkey, (2) a volcanic deformation in Domuyo, Argentina, (3) a synthetic slow-slip event and (4) an interseismic deformation around NAF in a descending frame in northern Turkey. Overall I show that my method is suitable for automated analysis of large, global InSAR datasets, and for robust detection and separation of deformation signals from nuisance signals in InSAR data