Inertial tracking is vital for robotic IoT and has gained popularity thanks to the ubiquity of low-cost inertial measurement units and deep learning-powered tracking algorithms. Existing works, however, have not fully utilized IMU measurements, particularly magnetometers, nor have they maximized the potential of deep learning to achieve the desired accuracy. To address these limitations, we introduce NeurIT, which elevates tracking accuracy to a new level. NeurIT employs a Time-Frequency Block-recurrent Transformer (TF-BRT) at its core, combining both RNN and Transformer to learn representative features in both time and frequency domains. To fully utilize IMU information, we strategically employ body-frame differentiation of magnetometers, considerably reducing the tracking error. We implement NeurIT on a customized robotic platform and conduct evaluation in various indoor environments. Experimental results demonstrate that NeurIT achieves a mere 1-meter tracking error over a 300-meter distance. Notably, it significantly outperforms state-of-the-art baselines by 48.21% on unseen data. Moreover, NeurIT demonstrates robustness in large urban complexes and performs comparably to the visual-inertial approach (Tango Phone) in vision-favored conditions while surpassing it in feature-sparse settings. We believe NeurIT takes an important step forward toward practical neural inertial tracking for ubiquitous and scalable tracking of robotic things. NeurIT is open-sourced here: https://github.com/aiot-lab/NeurIT.