One of the most striking findings in modern research on large language models (LLMs) is that, given a model and dataset of sufficient scale, scaling up compute at training time leads to better final results. However, there is also another lesser-mentioned scaling phenomenon, where adopting more sophisticated methods and/or scaling compute at inference time can result in significantly better output from LLMs. We will present a tutorial on past and present classes of generation algorithms for generating text from autoregressive LLMs, ranging from greedy decoding to sophisticated meta-generation algorithms used to power compound AI systems. We place a special emphasis on techniques for making these algorithms efficient, both in terms of token costs and generation speed. Our tutorial unifies perspectives from three research communities: traditional natural language processing, modern LLMs, and machine learning systems. In turn, we aim to make attendees aware of (meta-)generation algorithms as a promising direction for improving quality, increasing diversity, and enabling resource-constrained research on LLMs.