Few-shot learning (FSL) is an important and topical problem in computer vision that has motivated extensive research into numerous methods spanning from sophisticated meta-learning methods to simple transfer learning baselines. We seek to push the limits of a simple-but-effective pipeline for more realistic and practical settings of few-shot image classification. To this end, we explore few-shot learning from the perspective of neural network architecture, as well as a three stage pipeline of network updates under different data supplies, where unsupervised external data is considered for pre-training, base categories are used to simulate few-shot tasks for meta-training, and the scarcely labelled data of an novel task is taken for fine-tuning. We investigate questions such as: (1) How pre-training on external data benefits FSL? (2) How state-of-the-art transformer architectures can be exploited? and (3) How fine-tuning mitigates domain shift? Ultimately, we show that a simple transformer-based pipeline yields surprisingly good performance on standard benchmarks such as Mini-ImageNet, CIFAR-FS, CDFSL and Meta-Dataset. Our code and demo are available at https://hushell.github.io/pmf.