Abstract: Pre-trained language models (PLMs) may fail in giving reliable estimates of their predictive uncertainty. We take a close look into this problem, aiming to answer two questions: (1) Do PLMs learn to become calibrated in the training process? (2) How effective are existing calibration methods? For the first question, we conduct fine-grained control experiments to study the dynamic change in PLMs' calibration performance in training. We consider six factors as control variables, including dataset difficulty, available training samples, training steps, the number of tunable parameters, model scale, and pretraining. We observe a consistent change in calibration performance across six factors. We find that PLMs don't learn to become calibrated in training, evidenced by the continual increase in confidence, no matter whether the predictions are correct or not. We highlight that our finding somewhat contradicts two established conclusions: (a) Larger PLMs are more calibrated; (b) Pretraining improves model calibration. Next, we study the effectiveness of existing calibration methods in mitigating the overconfidence issue. Besides unlearnable calibration methods (e.g., label smoothing), we adapt and extend two recently proposed learnable methods that directly collect data to train models to have reasonable confidence estimations. Experimental results show that learnable methods significantly reduce PLMs' confidence in wrong predictions.