Large Language Model (LLM)-based agents have emerged as a new paradigm that extends LLMs' capabilities beyond text generation to dynamic interaction with external environments. By integrating reasoning with perception, memory, and tool use, agents are increasingly deployed in diverse domains like web navigation and household robotics. A critical challenge, however, lies in ensuring agent generalizability - the ability to maintain consistent performance across varied instructions, tasks, environments, and domains, especially those beyond agents' fine-tuning data. Despite growing interest, the concept of generalizability in LLM-based agents remains underdefined, and systematic approaches to measure and improve it are lacking. In this survey, we provide the first comprehensive review of generalizability in LLM-based agents. We begin by emphasizing agent generalizability's importance by appealing to stakeholders and clarifying the boundaries of agent generalizability by situating it within a hierarchical domain-task ontology. We then review datasets, evaluation dimensions, and metrics, highlighting their limitations. Next, we categorize methods for improving generalizability into three groups: methods for the backbone LLM, for agent components, and for their interactions. Moreover, we introduce the distinction between generalizable frameworks and generalizable agents and outline how generalizable frameworks can be translated into agent-level generalizability. Finally, we identify critical challenges and future directions, including developing standardized frameworks, variance- and cost-based metrics, and approaches that integrate methodological innovations with architecture-level designs. By synthesizing progress and highlighting opportunities, this survey aims to establish a foundation for principled research on building LLM-based agents that generalize reliably across diverse applications.