Recent advancements in Large Language Models (LLMs) have led to a rapid growth of agentic systems capable of handling a wide range of complex tasks. However, current research largely relies on manual, task-specific design, limiting their adaptability to novel tasks. In this paper, we introduce a new research problem: Modularized LLM Agent Search (MoLAS). We propose a modular design space that abstracts existing LLM agent designs into four fundamental modules with uniform IO interface: Planning, Reasoning, Tool Use, and Memory. Building on this design space, we present a novel LLM agent search framework called AgentSquare, which introduces two core mechanisms, i.e., module evolution and recombination, to efficiently search for optimized LLM agents. To further accelerate the process, we design a performance predictor that uses in-context surrogate models to skip unpromising agent designs. Extensive experiments across six benchmarks, covering the diverse scenarios of web, embodied, tool use and game applications, show that AgentSquare substantially outperforms hand-crafted agents, achieving an average performance gain of 17.2% against best-known human designs. Moreover, AgentSquare can generate interpretable design insights, enabling a deeper understanding of agentic architecture and its impact on task performance. We believe that the modular design space and AgentSquare search framework offer a platform for fully exploiting the potential of prior successful designs and consolidating the collective efforts of research community. Code repo is available at https://github.com/tsinghua-fib-lab/AgentSquare.