Natural language processing (NLP) has witnessed a profound impact of large language models (LLMs) that excel in a multitude of tasks. However, the limitation of LLMs in multilingual settings, particularly in underrepresented languages, remains a significant hurdle. This thesis aims to bridge the gap in NLP research and development by focusing on underrepresented languages. A comprehensive evaluation of LLMs is conducted to assess their capabilities in these languages, revealing the challenges of multilingual and multicultural generalization. Addressing the multilingual generalization gap, this thesis proposes data-and-compute-efficient methods to mitigate the disparity in LLM ability in underrepresented languages, allowing better generalization on underrepresented languages without the loss of task generalization ability. The proposed solutions cover cross-lingual continual instruction tuning, retrieval-based cross-lingual in-context learning, and in-context query alignment. Furthermore, a novel method to measure cultural values alignment between LLMs operating in different languages is proposed, ensuring cultural sensitivity and inclusivity. These contributions aim to enhance the multilingual and multicultural alignment of LLMs in underrepresented languages, ultimately advancing the NLP field toward greater equality and inclusiveness.