Neural machine translation (MT) models achieve strong results across a variety of settings, but it is widely believed that they are highly sensitive to "noisy" inputs, such as spelling errors, abbreviations, and other formatting issues. In this paper, we revisit this insight in light of recent multilingual MT models and large language models (LLMs) applied to machine translation. Somewhat surprisingly, we show through controlled experiments that these models are far more robust to many kinds of noise than previous models, even when they perform similarly on clean data. This is notable because, even though LLMs have more parameters and more complex training processes than past models, none of the open ones we consider use any techniques specifically designed to encourage robustness. Next, we show that similar trends hold for social media translation experiments -- LLMs are more robust to social media text. We include an analysis of the circumstances in which source correction techniques can be used to mitigate the effects of noise. Altogether, we show that robustness to many types of noise has increased.