This chapter explores different topics. First how large language models (LLMs) can improve a global optimizer, and second how optimizer through prompt optimization can improve the performance of LLMs on a range of tasks. Particularly important, given the general topic of the book, is the observation that LLMs have demonstrated capabilities across a range of tasks. This leads to a dilemma and presents significant variation in their cost and performance: Is the most capable LLM also the most expensive? Routing queries across LLMs is an emerging and challenging problem, because the routing system has to infer the characteristics of the query and the capability of LLMs into a set to respond to it. Routing queries among LLMs shows some commonalities with multi-fidelity and multiple information source optimization, as envisaged and discussed at the end of this chapter.