Intelligent systems powered by machine learning are ubiquitous today. However, their current rigid design fails and requires dedicated efforts to cater to ever-changing data, use cases, and deployment settings. In this talk, I will present my work towards enabling adaptive machine learning solutions for flexible and seamless deployment across widely changing scenarios through the lens of web search. First, I present Matryoshka embeddings for adaptive data representations that can power web-scale adaptive retrieval. Next, I extend these principles to the neural networks, crafting MatFormer models that adapt their computational footprint based on input and device with minimal overhead during deployment. Further, to address the inherent rigidity in the design of web search systems, I will dive into differentiable search solutions, fundamentally rethinking how large-scale AI pipelines harness data for continuous improvement. Finally, I conclude with future works directed towards adaptive contextual and continual intelligence across disciplines.