Vision-Language Models (VLMs), exemplified by CLIP, have emerged as foundational for multimodal intelligence. However, their capacity for logical understanding remains significantly underexplored, resulting in critical ''logical blindspots'' that limit their reliability in practical applications. To systematically diagnose this, we introduce LogicBench, a comprehensive benchmark with over 50,000 vision-language pairs across 9 logical categories and 4 diverse scenarios: images, videos, anomaly detection, and medical diagnostics. Our evaluation reveals that existing VLMs, even the state-of-the-art ones, fall at over 40 accuracy points below human performance, particularly in challenging tasks like Causality and Conditionality, highlighting their reliance on surface semantics over critical logical structures. To bridge this gap, we propose LogicCLIP, a novel training framework designed to boost VLMs' logical sensitivity through advancements in both data generation and optimization objectives. LogicCLIP utilizes logic-aware data generation and a contrastive learning strategy that combines coarse-grained alignment, a fine-grained multiple-choice objective, and a novel logical structure-aware objective. Extensive experiments demonstrate LogicCLIP's substantial improvements in logical comprehension across all LogicBench domains, significantly outperforming baselines. Moreover, LogicCLIP retains, and often surpasses, competitive performance on general vision-language benchmarks, demonstrating that the enhanced logical understanding does not come at the expense of general alignment. We believe that LogicBench and LogicCLIP will be important resources for advancing VLM logical capabilities.