Earth observation (EO) satellite missions have been providing detailed images about the state of the Earth and its land cover for over 50 years. Long term missions, such as NASA's Landsat, Terra, and Aqua satellites, and more recently, the ESA's Sentinel missions, record images of the entire world every few days. Although single images provide point-in-time data, repeated images of the same area, or satellite image time series (SITS) provide information about the changing state of vegetation and land use. These SITS are useful for modeling dynamic processes and seasonal changes such as plant phenology. They have potential benefits for many aspects of land and natural resource management, including applications in agricultural, forest, water, and disaster management, urban planning, and mining. However, the resulting satellite image time series (SITS) are complex, incorporating information from the temporal, spatial, and spectral dimensions. Therefore, deep learning methods are often deployed as they can analyze these complex relationships. This review presents a summary of the state-of-the-art methods of modelling environmental, agricultural, and other Earth observation variables from SITS data using deep learning methods. We aim to provide a resource for remote sensing experts interested in using deep learning techniques to enhance Earth observation models with temporal information. In this review, we are primarily concerned with methods of estimating or predicting EO variables from SITS data. These can be divided into two types of tasks depending on the nature of the variable being estimated. If the variable can take one of two or more discrete values, then the task is classification. Examples of classification tasks include land cover mapping [1], crop type identification [2], and burnt area mapping [3]. If the variable can take continuous numeric values, then the task is regression. In the context of time series, regression tasks can be further categorized as extrinsic regression tasks, which estimate the value of a variable external to those represented by the time series [4], or forecasting tasks, which predict future values of a time series based on its historical values. While classification and extrinsic regression tasks are technically distinct, in practice many of the deep learning methods used are very similar. Many architectures that have originally been designed for a classification task can easily be adapted for extrinsic regression tasks (and vice versa) [5], for example, by modifying the last layer and the loss function. A more important consideration when considering deep learning architectures for SITS tasks is the quantity of labeled data available for training models. Many deep learning models have thousands or even millions of parameters that need estimating and thus training these models require large quantities of labeled data. Smaller architectures with fewer parameters are likely to be more suitable when labeled data are limited. In particular, techniques such as semi-supervised and unsupervised learning are designed for situations with few or no labeled samples, respectively. In related work, Gómez et al. [1] provided a comprehensive review of using optical SITS data for land cover classification. However, there have been developments in EO data and machine learning since that review that have led to a substantial increase in SITS research and its potential applications for EO monitoring. One reason for these recent developments is the availability of data from the ESA Sentinel missions that provide both optical and synthetic aperture radar (SAR) data at higher temporal and spatial resolution than many of the previously readily available sources. Another reason is the wide variety of machine learning methods, especially deep learning methods, that can model the complex relationships that exist between the observed electromagnetic radiation and the variable of interest. Both these advances mean there are a wider variety of techniques available for EO modelling and a wider variety of tasks that can be performed using these models. The current review, which covers the use of deep learning methods for SITS, therefore provides an update to review [1]. It focuses on deep learning analysis of SITS for classification and extrinsic regression problems and examines a broad range of applications of SITS data, thus filling the gap left by these other recent reviews. However, the review excludes DL forecasting applications of SITS, as these have been extensively covered by Moskolaï et al. [6]. As we are interested in modelling of temporal features, we limit the study to time series longer than two. Thus, we exclude methods such as bitemporal change detection, which identifies differences in two images obtained at separate times. A recent review of change detection in remote sensing is provided in [7]. SELECTION PRINCIPLES AND RELATED SURVEYS SELECTION PRINCIPLES There are more studies using deep learning for SITS than can feasibly be included in a single review, thus this review is not an exhaustive survey. However, we aim to provide coverage of a broad range of studies that show both the deep learning methods applied to SITS and the tasks for which SITS have been used. We have therefore included studies that: 1) are the key works developing DL techniques for SITS tasks, 2) show how the various DL methods have been applied to SITS, 3) provide insight into extracting temporal and/or spatial features from SITS, and 4) highlight the wide range of tasks for which SITS can be used. Papers were mainly found by searching on