We propose DeltaStreamer, a novel agentic framework for streaming video understanding inspired by how humans observe, remember, and investigate. Streaming video understanding requires a system to retain evidence before knowing which details future queries will need. Existing approaches often obscure event transitions and omit relevant details when compressing video history, and cannot recover missing visual evidence. DeltaStreamer addresses these limitations by combining change-aware memory with query-driven planning and targeted evidence gathering with replay. Before a query arrives, it continuously observes the stream and explicitly records visual changes in structured memory, preserving how events unfold rather than only what is present. When a query arrives, a query-driven planner identifies the required evidence and guides memory retrieval and targeted replay. By revisiting historical frames, the agent can recover visual details omitted during observation and ground its answer in evidence beyond the retained descriptions. This connects continuous observation with active investigation tailored to each question. Experiments on OVO-Bench and StreamingBench demonstrate improvements over representative streaming video understanding methods, with overall scores of 66.07% and 59.53%, respectively. Project page: https://bbbbchan.github.io/DeltaStreamer/