Large language models (LLMs) are reshaping automated program repair. We present a unified taxonomy that groups 62 recent LLM-based repair systems into four paradigms defined by parameter adaptation and control authority over the repair loop, and overlays two cross-cutting layers for retrieval and analysis augmentation. Prior surveys have either focused on classical software repair techniques, on LLMs in software engineering more broadly, or on subsets of LLM-based software repair, such as fine-tuning strategies or vulnerability repair. We complement these works by treating fine-tuning, prompting, procedural pipelines, and agentic frameworks as first-class paradigms and systematically mapping representative systems to each of these paradigms. We also consolidate evaluation practice on common benchmarks by recording benchmark scope, pass@k, and fault-localization assumptions to support a more meaningful comparison of reported success rates. We clarify trade-offs among paradigms in task alignment, deployment cost, controllability, and ability to repair multi-hunk or cross-file bugs. We discuss challenges in current LLM-based software repair and outline research directions. Our artifacts, including the representation papers and scripted survey pipeline, are publicly available at this https URL.

Within the realm of software engineering, specialized tasks on code, such as program repair, present unique challenges, necessitating fine-tuning Large language models~(LLMs) to unlock state-of-the-art performance. Fine-tuning approaches proposed in the literature for LLMs on program repair tasks generally overlook the need to reason about the logic behind code changes, beyond syntactic patterns in the data. High-performing fine-tuning experiments also usually come at very high computational costs. With MORepair, we propose a novel perspective on the learning focus of LLM fine-tuning for program repair: we not only adapt the LLM parameters to the syntactic nuances of the task of code transformation (objective 1), but we also specifically fine-tune the LLM with respect to the logical reason behind the code change in the training data (objective 2). Such a multi-objective fine-tuning will instruct LLMs to generate high-quality patches. We apply MORepair to fine-tune four open-source LLMs with different sizes and architectures. Experimental results on function-level and repository-level repair benchmarks show that the implemented fine-tuning effectively boosts LLM repair performance by 11.4% to 56.0%. We further show that our fine-tuning strategy yields superior performance compared to the state-of-the-art approaches, including standard fine-tuning, Fine-tune-CoT, and RepairLLaMA.