Recent advances in large language models (LLMs) have demonstrated potential for LLM agents. To facilitate the training for these agents with both linguistic feedback and non-linguistic reward signals, we introduce Learning through Communication (LTC). We design a universal buffer to store all the feedback, and an iterative pipeline to enable an LLM agent to explore and update its policy in an given environment. To optimize agent interactions for task-specific learning with our universal buffer and pipeline, we introduce diverse communication patterns tailored for both single-agent and multi-agent environments. We evaluate the efficacy of our LTC approach on four diverse datasets: ALFWorld (single-agent), HotpotQA (multi-agent collaboration), Chameleon (multi-agent competition), and GSM8k (multi-agent teacher-student). On these data sets, LTC outperforms the supervised instruction fine-tuning baselines by 3.6% to 12%. These results highlight the versatility and efficiency of LTC in facilitating online adaptation for LLM agents.