The recent emergence of Multi-modal Large Language Models (MLLMs) has introduced a new dimension to the Text-rich Image Understanding (TIU) field, with models demonstrating impressive and inspiring performance. However, their rapid evolution and widespread adoption have made it increasingly challenging to keep up with the latest advancements. To address this, we present a systematic and comprehensive survey to facilitate further research on TIU MLLMs. Initially, we outline the timeline, architecture, and pipeline of nearly all TIU MLLMs. Then, we review the performance of selected models on mainstream benchmarks. Finally, we explore promising directions, challenges, and limitations within the field.