The Earth's surface is subject to complex and dynamic processes, ranging from large-scale phenomena such as tectonic plate movements to localized changes associated with ecosystems, agriculture, or human activity. Satellite images enable global monitoring of these processes with extensive spatial and temporal coverage, offering advantages over in-situ methods. In particular, resulting satellite image time series (SITS) datasets contain valuable information. To handle their large volume and complexity, some recent works focus on the use of graph-based techniques that abandon the regular Euclidean structure of satellite data to work at an object level. Besides, graphs enable modelling spatial and temporal interactions between identified objects, which are crucial for pattern detection, classification and regression tasks. This paper is an effort to examine the integration of graph-based methods in spatio-temporal remote-sensing analysis. In particular, it aims to present a versatile graph-based pipeline to tackle SITS analysis. It focuses on the construction of spatio-temporal graphs from SITS and their application to downstream tasks. The paper includes a comprehensive review and two case studies, which highlight the potential of graph-based approaches for land cover mapping and water resource forecasting. It also discusses numerous perspectives to resolve current limitations and encourage future developments.