Title: FoveaTer: Foveated Transformer for Image Classification. Abstract: Many animals and humans process the visual field with varying spatial resolution (foveated vision) and use peripheral processing to make eye movements and point the fovea to acquire high-resolution information about objects of interest. This architecture results in computationally efficient rapid scene exploration. Recent progress in self-attention-based vision Transformers, an alternative to the traditionally convolution-reliant computer vision systems, allows global interactions between feature locations and increases robustness to adversarial attacks. However, the Transformer models do not explicitly model the foveated properties of the visual system nor the interaction between eye movements and the classification task. We propose Foveated Transformer (FoveaTer) model, which uses pooling regions and eye movements to perform object classification tasks using a Vision Transformer architecture. Using square pooling regions or biologically-inspired radial-polar pooling regions, our proposed model pools the image features from the convolution backbone and uses the pooled features as an input to transformer layers. It decides on subsequent fixation location based on the attention assigned by the Transformer to various locations from past and present fixations. The model uses a confidence threshold to stop scene exploration. It dynamically allocates more fixation/computational resources to more challenging images before making the final image category decision. We construct a Foveated model using our proposed approach and compare it against a Baseline model, which does not contain any pooling. Using five ablation studies, we evaluate the contribution of different components of the Foveated model. We perform a psychophysics scene categorization task and use the experimental data to find a suitable radial-polar pooling region combination. We also show that the Foveated model better explains the human decisions in a scene categorization task than a Baseline model. On the ImageNet dataset, the Foveated model with Dynamic-stop achieves an accuracy of $8\%$ below the Baseline model with a throughput gain of $76\%$. Using a Foveated model with Dynamic-stop and the Baseline model, the ensemble achieves an accuracy of $0.7\%$ below the Baseline using the same throughput. We demonstrate our model's robustness against PGD adversarial attacks with both types of pooling regions, where we see the Foveated model outperform the Baseline model.