Imagine a world where AI can write code in any language, not just the popular ones. This is the promise of Large Language Models (LLMs) like those powering tools like GitHub Copilot. While LLMs excel with common languages like Python, they struggle with the unique challenges of low-resource programming languages (LRPLs) like Rust and R, and domain-specific languages (DSLs) used in niche areas like hardware design or finance. Why? These languages have far less data available for training, and DSLs often feature specialized syntax and semantics that general-purpose LLMs aren't equipped to handle. This limitation impacts millions of developers who could benefit from AI assistance. A new research survey dives deep into this problem, exploring the current landscape of LLM-based code generation for LRPLs and DSLs. The study reveals that researchers are tackling these challenges through innovative methods. Fine-tuning existing LLMs on specialized datasets has yielded some success, as has using clever prompting strategies to guide the AI. One approach uses the LLVM compiler's intermediate representation as a common language to help LLMs understand the connections between different languages. However, building suitable datasets is a major hurdle. Existing datasets are often scarce or unsuitable. Some researchers are creating synthetic data using LLMs like ChatGPT, while others meticulously curate smaller, high-quality datasets by hand. The lack of standard benchmarks also poses a problem. Without a common yardstick, comparing the effectiveness of different approaches becomes difficult. While MultiPL-E exists for some LRPLs, many DSLs lack such benchmarks, hindering progress. This research highlights the growing interest in extending LLM capabilities beyond mainstream programming languages, emphasizing the need for better data, benchmarks, and specialized techniques. As LLMs evolve, expect to see AI-powered coding tools become even more versatile and powerful, empowering developers across a wider range of languages and domains.