Leveraging large language models (LLMs) for complex natural language tasks typically requires long-form prompts to convey detailed requirements and information, which results in increased memory usage and inference costs. To mitigate these challenges, multiple efficient methods have been proposed, with prompt compression gaining significant research interest. This survey provides an overview of prompt compression techniques, categorized into hard prompt methods and soft prompt methods. First, the technical approaches of these methods are compared, followed by an exploration of various ways to understand their mechanisms, including the perspectives of attention optimization, Parameter-Efficient Fine-Tuning (PEFT), modality integration, and new synthetic language. We also examine the downstream adaptations of various prompt compression techniques. Finally, the limitations of current prompt compression methods are analyzed, and several future directions are outlined, such as optimizing the compression encoder, combining hard and soft prompts methods, and leveraging insights from multimodality.