Despite the superior performance, Large Language Models (LLMs) require significant computational resources for deployment and use. To overcome this issue, quantization methods have been widely applied to reduce the memory footprint of LLMs as well as increase the inference rate. However, a major challenge is that low-bit quantization methods often lead to performance degradation. It is important to understand how quantization impacts the capacity of LLMs. Different from previous studies focused on overall performance, this work aims to investigate the impact of quantization on emergent abilities, which are important characteristics that distinguish LLMs from small language models. Specifically, we examine the abilities of in-context learning, chain-of-thought reasoning, and instruction-following in quantized LLMs. Our empirical experiments show that these emergent abilities still exist in 4-bit quantization models, while 2-bit models encounter severe performance degradation on the test of these abilities. To improve the performance of low-bit models, we conduct two special experiments: (1) fine-gained impact analysis that studies which components (or substructures) are more sensitive to quantization, and (2) performance compensation through model fine-tuning. Our work derives a series of important findings to understand the impact of quantization on emergent abilities and sheds light on the possibilities of extremely low-bit quantization for LLMs.