Contrastive Language-Image Pre-training (CLIP) learns robust visual models through language supervision, making it a crucial visual encoding technique for various applications. However, CLIP struggles with comprehending spatial concepts in images, potentially restricting the spatial intelligence of CLIP-based AI systems. In this work, we propose SpatialCLIP, an enhanced version of CLIP with better spatial understanding capabilities. To capture the intricate 3D spatial relationships in images, we improve both "visual model" and "language supervision" of CLIP. Specifically, we design 3D-inspired ViT to replace the standard ViT in CLIP. By lifting 2D image tokens into 3D space and incorporating design insights from point cloud networks, our visual model gains greater potential for spatial perception. Meanwhile, captions with accurate and detailed spatial information are very rare. To explore better language supervision for spatial understanding, we re-caption images and perturb their spatial phrases as negative descriptions, which compels the visual model to seek spatial cues to distinguish these hard negative captions. With the enhanced visual model, we introduce SpatialLLaVA, following the same LLaVA-1.5 training protocol, to investigate the importance of visual representations for MLLM's spatial intelligence. Furthermore, we create SpatialBench, a benchmark specifically designed to evaluate CLIP and MLLM in spatial reasoning. SpatialCLIP and SpatialLLaVA achieve substantial performance improvements, demonstrating stronger capabilities in spatial perception and reasoning, while maintaining comparable results on general-purpose benchmarks.