Foundation models have reshaped AI by unifying fragmented architectures into scalable backbones with multimodal reasoning and contextual adaptation. In parallel, the long-standing notion of AI agents, defined by the sensing-decision-action loop, is entering a new paradigm: with FMs as their cognitive core, agents transcend rule-based behaviors to achieve autonomy, generalization, and self-reflection. This dual shift is reinforced by real-world demands such as autonomous driving, robotics, virtual assistants, and GUI agents, as well as ecosystem advances in embedded hardware, edge computing, mobile deployment platforms, and communication protocols that together enable large-scale deployment. Yet this convergence collides with reality: while applications demand long-term adaptability and real-time interaction, mobile and edge deployments remain constrained by memory, energy, bandwidth, and latency. This creates a fundamental tension between the growing complexity of FMs and the limited resources of deployment environments. This survey provides the first systematic characterization of adaptive, resource-efficient agentic AI systems. We summarize enabling techniques into elastic inference, test-time adaptation, dynamic multimodal integration, and agentic AI applications, and identify open challenges in balancing accuracy-latency-communication trade-offs and sustaining robustness under distribution shifts. We further highlight future opportunities in algorithm-system co-design, cognitive adaptation, and collaborative edge deployment. By mapping FM structures, cognition, and hardware resources, this work establishes a unified perspective toward scalable, adaptive, and resource-efficient agentic AI. We believe this survey can help readers to understand the connections between enabling technologies while promoting further discussions on the fusion of agentic intelligence and intelligent agents.