Code-mixing and code-switching (CSW) remain challenging phenomena for large language models (LLMs). Despite recent advances in multilingual modeling, LLMs often struggle in mixed-language settings, exhibiting systematic degradation in grammaticality, factuality, and safety behavior. This work provides a comprehensive overview of CSW research in modern large language model settings. We introduce a unifying taxonomy that organizes prior work along dimensions of data, modeling, and evaluation, and we distill these findings into a practical playbook of actionable recommendations for building, adapting, and evaluating CSW-capable LLMs. We review modeling approaches ranging from CSW-tailored pre-training and task-specific post-training to prompting strategies and in-context learning. We analyze current evaluation practices, highlighting sources of instability and limited reproducibility, and we catalog existing benchmarks while critically examining their linguistic coverage and English-centric biases. Finally, we discuss emerging safety concerns, including use of code-mixing as a mechanism for bypassing model safeguards, and identify open research challenges.