While Digital Twins are traditionally associated with domains of human-made systems, Earth Science Digital Twins (ESDTs) have been rising in popularity. ESDT represents a twin of a natural entity or ecosystem at a local, regional, or global scale, such as a river, a forest, an ocean, or the Earth itself. In this work, we conduct a systematic literature review of the existing ESDT systems. We identify the main ESDT domains as hydrology, geology, ecology, Earth, and atmosphere. We analyse the purposes of ESDTs, describe the software development tools that are often employed in ESDT development, and discuss the challenges and limitations that are specific to ESDTs. We conclude that data collection and computation limitations are among the most prominent, and maintaining the real-time mirror of the physical entity remains a challenge.