The lifelong learning paradigm in machine learning is an attractive alternative to the more prominent isolated learning scheme not only due to its resemblance to biological learning but also its potential to reduce energy waste by obviating excessive model re-training. A key challenge to this paradigm is the phenomenon of catastrophic forgetting. With the increasing popularity and success of pre-trained models in machine learning, we pose the question: What role does pre-training play in lifelong learning, specifically with respect to catastrophic forgetting? We investigate existing methods in the context of large, pre-trained models and evaluate their performance on a variety of text and image classification tasks, including a large-scale study using a novel data set of 15 diverse NLP tasks. Across all settings, we observe that generic pre-training implicitly alleviates the effects of catastrophic forgetting when learning multiple tasks sequentially compared to randomly initialized models. We then further investigate why pre-training alleviates forgetting in this setting. We study this phenomenon by analyzing the loss landscape, finding that pre-trained weights appear to ease forgetting by leading to wider minima. Based on this insight, we propose jointly optimizing for current task loss and loss basin sharpness to explicitly encourage wider basins during sequential fine-tuning. We show that this optimization approach outperforms several state-of-the-art task-sequential continual learning algorithms across multiple settings, occasionally even without retaining a memory that scales in size with the number of tasks.