Ancient scripts, e.g., Egyptian hieroglyphs, Oracle Bone Inscriptions, and Ancient Greek inscriptions, serve as vital carriers of human civilization, embedding invaluable historical and cultural information. Automating ancient script image recognition has gained importance, enabling large-scale interpretation and advancing research in archaeology and digital humanities. With the rise of deep learning, this field has progressed rapidly, with numerous script-specific datasets and models proposed. While these scripts vary widely, spanning phonographic systems with limited glyphs to logographic systems with thousands of complex symbols, they share common challenges and methodological overlaps. Moreover, ancient scripts face unique challenges, including imbalanced data distribution and image degradation, which have driven the development of various dedicated methods. This survey provides a comprehensive review of ancient script image recognition methods. We begin by categorizing existing studies based on script types and analyzing respective recognition methods, highlighting both their differences and shared strategies. We then focus on challenges unique to ancient scripts, systematically examining their impact and reviewing recent solutions, including few-shot learning and noise-robust techniques. Finally, we summarize current limitations and outline promising future directions. Our goal is to offer a structured, forward-looking perspective to support ongoing advancements in the recognition, interpretation, and decipherment of ancient scripts.