Visual speech recognition (VSR), also known as lip reading, is the task of recognizing speech from silent video. Despite significant advancements in VSR over recent decades, most existing methods pay limited attention to real-world visual challenges such as illumination variations, occlusions, blurring, and pose changes. To address these challenges, we propose GLip, a Global-Local Integrated Progressive framework designed for robust VSR. GLip is built upon two key insights: (i) learning an initial coarse alignment between visual features across varying conditions and corresponding speech content facilitates the subsequent learning of precise visual-to-speech mappings in challenging environments; (ii) under adverse conditions, certain local regions (e.g., non-occluded areas) often exhibit more discriminative cues for lip reading than global features. To this end, GLip introduces a dual-path feature extraction architecture that integrates both global and local features within a two-stage progressive learning framework. In the first stage, the model learns to align both global and local visual features with corresponding acoustic speech units using easily accessible audio-visual data, establishing a coarse yet semantically robust foundation. In the second stage, we introduce a Contextual Enhancement Module (CEM) to dynamically integrate local features with relevant global context across both spatial and temporal dimensions, refining the coarse representations into precise visual-speech mappings. Our framework uniquely exploits discriminative local regions through a progressive learning strategy, demonstrating enhanced robustness against various visual challenges and consistently outperforming existing methods on the LRS2 and LRS3 benchmarks. We further validate its effectiveness on a newly introduced challenging Mandarin dataset.