Large language models (LLMs) are introducing a paradigm shift in molecular discovery by enabling text-guided interaction with chemical spaces through natural language and symbolic notations, with emerging extensions to incorporate multi-modal inputs. To advance this emerging field, this survey provides an up-to-date and forward-looking review of the emerging use of LLMs for two central tasks: molecule generation and molecule optimization. We organize our survey around four fundamental challenges that have emerged as critical evaluation dimensions in recent studies: ensuring validity, enhancing synthesizability, achieving precise property control, and maximizing diversity. Based on this, we systematically analyze how current LLM learning paradigms are applied to tackle each challenge, revealing the distinct capabilities and inherent limitations of each approach. In addition, we include the commonly used datasets and evaluation protocols aligned with these challenges. We conclude by discussing future directions, positioning this survey as a resource for researchers working at the intersection of LLMs and molecular science. A continuously updated reading list is available at https://github.com/REAL-Lab-NU/Awesome-LLM-Centric-Molecular-Discovery.

In drug discovery, molecular optimization aims to iteratively refine a lead compound to improve molecular properties while preserving structural similarity to the original molecule. However, each oracle evaluation is expensive, making sample efficiency a key challenge for existing methods under a limited oracle budget. Trial-and-error approaches require many oracle calls, while methods that leverage external knowledge tend to reuse familiar templates and struggle on challenging objectives. A key missing piece is long-term memory that can ground decisions and provide reusable insights for future optimizations. To address this, we present MolMem (Molecular optimization with Memory), a multi-turn agentic reinforcement learning (RL) framework with a dual-memory system. Specifically, MolMem uses Static Exemplar Memory to retrieve relevant exemplars for cold-start grounding, and Evolving Skill Memory to distill successful trajectories into reusable strategies. Built on this memory-augmented formulation, we train the policy with dense step-wise rewards, turning costly rollouts into long-term knowledge that improves future optimization. Extensive experiments show that MolMem achieves 90% success on single-property tasks (1.5× over the best baseline) and 52% on multi-property tasks using only 500 oracle calls. Our code is available at https://github.com/REAL-Lab-NU/MolMem.