This paper presents Agent-Based Software Engineering (SE) 3.0, a new era in which intelligent agents are responsible for achieving complex, goal-oriented software engineering (SE) objectives, rather than simply generating code. Leveraging these new capabilities while ensuring trustworthiness requires recognizing the fundamental duality of the SE field, which consists of two complementary approaches: SE for humans and SE for agents. This duality requires a fundamental reimagining of the fundamental elements of SE (actors, processes, tools, and artifacts), manifesting differently in each approach. To support this, we propose two purpose-driven workbenches: the Agent Command Environment (ACE) and the Agent Execution Environment (AEE). The ACE serves as a command center where humans coordinate and guide agent teams, while the AEE is a digital workspace where agents perform their tasks, leveraging human expertise when faced with ambiguous or complex trade-offs. This bidirectional partnership, which supports agent-initiated human callbacks and handoffs, fosters new structured engineering activities (i.e., processes) that redefine human-AI collaboration and advance the evolution from agent coding to truly agent-based software engineering. The paper concludes with a vision for Structured Agent-Based SE (SASE), outlines some fundamental elements for the future of SE, and concludes with a research roadmap that identifies key challenges and opportunities. The goal is not to provide definitive solutions, but rather to provide a conceptual foundation and structured vocabulary to encourage the SE community to move beyond existing human-centric principles and toward a disciplined, scalable, and trustworthy agent-based future.