Generative information extraction (Generative IE) aims to generate structured text sequences from unstructured text using a generative framework. Scaling in model size yields variations in adaptation and generalization, and also drives fundamental shifts in the techniques and approaches used within this domain. In this survey, we first review generative information extraction (IE) methods based on pre-trained language models (PLMs) and large language models (LLMs), focusing on their adaptation and generalization capabilities. We also discuss the connection between these methods and these two aspects. Furthermore, to balance task performance with the substantial computational demands associated with LLMs, we emphasize the importance of model collaboration. Finally, given the advanced capabilities of LLMs, we explore methods for integrating diverse IE tasks into unified models.