Large language models (LLMs) show remarkable human-like capability in various domains and languages. To bridge this quality gap, we introduce Cendol, a collection of Indonesian LLMs encompassing both decoder-only and encoder-decoder architectures across a range of model sizes. We highlight Cendol's effectiveness across a diverse array of tasks, attaining ~20% improvement, and demonstrate its capability to generalize to unseen tasks and indigenous languages of Indonesia. Furthermore, Cendol models showcase improved human favorability despite their limitations in capturing indigenous knowledge and cultural values in Indonesia. In addition, we discuss the shortcomings of parameter-efficient tunings, such as LoRA, for language adaptation. Alternatively, we propose the usage of vocabulary adaptation to enhance efficiency. Lastly, we evaluate the safety of Cendol and showcase that safety in pre-training in one language such as English is transferable to low-resource languages, such as Indonesian, even without RLHF and safety fine-tuning.