Learning-to-rank (LTR) algorithms aim to order a set of items according to some criteria. They are at the core of applications such as web search and social media recommendations, and are an area of rapidly increasing interest, with the rise of large language models (LLMs) and the widespread impact of these technologies on society. In this paper, we survey the diverse use cases of LTR methods in natural language processing (NLP) research, looking at previously under-studied aspects such as multilingualism in LTR applications and statistical significance testing for LTR problems. We also consider how large language models are changing the LTR landscape. This survey is aimed at NLP researchers and practitioners interested in understanding the formalisms and best practices regarding the application of LTR approaches in their research.