With the ever growing scale of neural models, knowledge distillation (KD) attracts more attention as a prominent tool for neural model compression. However, there are counter intuitive observations in the literature showing some challenging limitations of KD. A case in point is that the best performing checkpoint of the teacher might not necessarily be the best teacher for training the student in KD. Therefore, one important question would be how to find the best checkpoint of the teacher for distillation? Searching through the checkpoints of the teacher would be a very tedious and computationally expensive process, which we refer to as the checkpoint-search problem. Moreover, another observation is that larger teachers might not necessarily be better teachers in KD, which is referred to as the capacity-gap problem. To address these challenging problems, in this work, we introduce our progressive knowledge distillation (Pro-KD) technique which defines a smoother training path for the student by following the training footprints of the teacher instead of solely relying on distilling from a single mature fully-trained teacher. We demonstrate that our technique is quite effective in mitigating the capacity-gap problem and the checkpoint search problem. We evaluate our technique using a comprehensive set of experiments on different tasks such as image classification (CIFAR-10 and CIFAR-100), natural language understanding tasks of the GLUE benchmark, and question answering (SQuAD 1.1 and 2.0) using BERT-based models and consistently got superior results over state-of-the-art techniques.