Active visual exploration aims to assist an agent with a limited field of view to understand its environment based on partial observations made by choosing the best viewing directions in the scene. Recent methods have tried to address this problem either by using reinforcement learning, which is difficult to train, or by uncertainty maps, which are task-specific and can only be implemented for dense prediction tasks. In this paper, we propose the Glimpse-Attend-and-Explore model which: (a) employs self-attention to guide the visual exploration instead of task-specific uncertainty maps; (b) can be used for both dense and sparse prediction tasks; and (c) uses a contrastive stream to further improve the representations learned. Unlike previous works, we show the application of our model on multiple tasks like reconstruction, segmentation and classification. Our model provides encouraging results while being less dependent on dataset bias in driving the exploration. We further perform an ablation study to investigate the features and attention learned by our model. Finally, we show that our self-attention module learns to attend different regions of the scene by minimizing the loss on the downstream task. Code: https://github.com/soroushseifi/glimpse-attend-explore.