Building agentic systems around frozen foundation models remains largely a craft: chains of thought, reflection loops, tool calls, and multi-agent topologies are assembled by hand. Automated Design of Agentic Systems (ADAS) recasts that craft as a search problem. In this paper we survey the ADAS literature from 2022 to 2026 through a unifying four-axis framework that re-casts the three classical pillars of neural architecture search (NAS) in an agentic setting: the optimization target (the prompt, the parameters of a compound system, the workflow topology, a modular cell, or full code), the search strategy (LLM-as-optimizer, textual gradients, evolutionary and quality-diversity search, MCTS, Bayesian or surrogate methods, and RL/DPO), the representation (a natural-language string, a modular DSL, a graph, or code), and the feedback signal (a scalar, a preference, a natural-language critique, a surrogate, or novelty). We classify thirty-three methods along these axes, spanning 2022 to 2026 and including the recent surge of 2026 work, trace two structural tensions—expressiveness versus searchability and feedback richness versus credit assignment—and examine evaluation practice, including cost, transfer, contamination, and reward hacking. We conclude with the safety problems that recursive self-improvement makes concrete and the open directions they impose.