Climate change poses a significant challenge to global agriculture. The sensitivity of agriculture to climate variations means it can either exacerbate climate change through greenhouse gas emissions from poor management practices or mitigate it by absorbing these gases through carbon capture. Adapting to climate impacts is not new, especially within the agricultural sector. However, the advent of Generative Artificial Intelligence (GenAI), specifically Language Models, presents a novel approach to adaptation in climate-smart agriculture. These models have the ability to analyze, synthesize, and process vast amounts of data from diverse fields such as climate science and agriculture. This chapter delves into this emerging field, examining the applications of LLMs in climate-smart agriculture, the challenges inherent in their use, and the strategic approaches necessary for their effective implementation. We begin with a historical overview that sets the stage for understanding the evolution from traditional to technology-driven agricultural practices. The core of the chapter explores how Language Models, including Generative AI and Large Language Models like ChatGPT, are poised to transform agricultural practices through advanced data analysis and decision-making support. Further, we assess the potential of Language Models to improve agricultural productivity and sustainability, discussing specific use cases such as pattern recognition, data processing, and enhanced communication. However, alongside the opportunities, we also address the significant challenges such as data privacy, bias, and the environmental impact of deploying these technologies at local to broad scale. Ultimately, this chapter provides a comprehensive guide to the next frontier in agriculture, offering insights into how Language Models can be strategically integrated to support climate resilience and smarter farming solutions.