For more efficient generalization to unseen domains (classes), most Few-shot Segmentation (FSS) would directly exploit pre-trained encoders and only fine-tune the decoder, especially in the current era of large models. However, such fixed feature encoders tend to be class-agnostic, inevitably activating objects that are irrelevant to the target class. In contrast, humans can effortlessly focus on specific objects in the line of sight. This paper mimics the visual perception pattern of human beings and proposes a novel and powerful prompt-driven scheme, called ``Prompt and Transfer" (PAT), which constructs a dynamic class-aware prompting paradigm to tune the encoder for focusing on the interested object (target class) in the current task. Three key points are elaborated to enhance the prompting: 1) Cross-modal linguistic information is introduced to initialize prompts for each task. 2) Semantic Prompt Transfer (SPT) that precisely transfers the class-specific semantics within the images to prompts. 3) Part Mask Generator (PMG) that works in conjunction with SPT to adaptively generate different but complementary part prompts for different individuals. Surprisingly, PAT achieves competitive performance on 4 different tasks including standard FSS, Cross-domain FSS (e.g., CV, medical, and remote sensing domains), Weak-label FSS, and Zero-shot Segmentation, setting new state-of-the-arts on 11 benchmarks.