What is the relationship between model architecture and the ability to perform in-context learning? In this empirical study, we take the first steps towards answering this question. In particular, we evaluate fifteen model architectures across a suite of synthetic in-context learning tasks. The selected architectures represent a broad range of paradigms, including recurrent and convolution-based neural networks, transformers, and state-space models. We discover that all considered architectures can perform in-context learning under certain conditions. However, contemporary architectures are found to be the best performing, especially as task complexity grows. Additionally, our follow-up experiments delve into various factors that influence in-context learning. We observe varied sensitivities among architectures with respect to hyperparameter settings. Our study of training dynamics reveals that certain architectures exhibit a smooth, progressive learning trajectory, while others demonstrate periods of stagnation followed by abrupt mastery of the task. Finally, and somewhat surprisingly, we find that several state-space model variants are more robust in-context learners than transformers; since state-space models have constant-sized memory footprints at inference time, this result opens the future possibility of scaling up in-context learning to vastly larger numbers of in-context examples.