Significant progress in multimodal large language models (MLLMs) has driven advances in visual question answering, visual understanding, and reasoning tasks, and their potential for deployment on resource-constrained edge devices is increasingly recognized. However, large model sizes and the substantial costs of deployment and inference remain major barriers to practical adoption. Optimizing MLLMs for edge devices has become a critical research direction in this field. A comprehensive survey of recent advances in optimizing MLLMs for edge deployment was presented, along with the associated challenges and development trends. The research evolution of MLLMs on edge devices was reviewed, with particular emphasis on model architecture optimization and inference scheduling strategies. In model architecture optimization, techniques including visual information compression, sparse attention, and mixture-of-experts models were specifically analyzed. System-level optimizations involving computation scheduling, hardware adaptation, compilation optimization, and cloud-edge collaboration were investigated to enhance inference efficiency and energy efficiency. Furthermore, the key challenges of these models in practical applications were discussed, and a variety of task scenarios ranging from assistive to collaborative and autonomous types were covered, categorized by the perspective of autonomy levels. Finally, current limitations were summarized and future research directions regarding standardized deployment, efficient computing and storage, and multi-modal fusion optimization were outlined.