Referring Multi-object tracking (RMOT) is an important research field in computer vision. Its task form is to guide the models to track the objects that conform to the language instruction. However, the RMOT task commonly requires clear language instructions, such methods often fail to work when complex language instructions with reasoning characteristics appear. In this work, we propose a new task, called Reasoning-based Multi-Object Tracking (ReaMOT). ReaMOT is a more challenging task that requires accurate reasoning about objects that match the language instruction with reasoning characteristic and tracking the objects' trajectories. To advance the ReaMOT task and evaluate the reasoning capabilities of tracking models, we construct ReaMOT Challenge, a reasoning-based multi-object tracking benchmark built upon 12 datasets. Specifically, it comprises 1,156 language instructions with reasoning characteristic, 423,359 image-language pairs, and 869 diverse scenes, which is divided into three levels of reasoning difficulty. In addition, we propose a set of evaluation metrics tailored for the ReaMOT task. Furthermore, we propose ReaTrack, a training-free framework for reasoning-based multi-object tracking based on large vision-language models (LVLM) and SAM2, as a baseline for the ReaMOT task. Extensive experiments on the ReaMOT Challenge benchmark demonstrate the effectiveness of our ReaTrack framework.