Recent advances in Pretrained Language Models (PLMs) and Large Language Models (LLMs) have demonstrated transformative capabilities across diverse domains. The field of patent analysis and innovation is not an exception, where natural language processing (NLP) techniques presents opportunities to streamline and enhance important tasks -- such as patent classification and patent retrieval -- in the patent cycle. This not only accelerates the efficiency of patent researchers and applicants, but also opens new avenues for technological innovation and discovery. Our survey provides a comprehensive summary of recent NLP-based methods -- including multimodal ones -- in patent analysis. We also introduce a novel taxonomy for categorization based on tasks in the patent life cycle, as well as the specifics of the methods. This interdisciplinary survey aims to serve as a comprehensive resource for researchers and practitioners who work at the intersection of NLP, Multimodal AI, and patent analysis, as well as patent offices to build efficient patent systems.