1) It takes your query, and given the complexity might expand it to several search queries using an LLM. ("rephrasing")
2) It runs queries against a web search index (I think it was using Bing or Brave at first, but they probably have their own by now), and uses an LLM to decide which are the best/most relevant documents. It starts writing a summary while it dives into sources (see next).
3) If necessary it will download full source documents that popped up in search to seed the context when generating a more in-depth summary/answer. They do this themselves because using OpenAI to do it is far more expensive.
#3 is the problem. Especially because SEO has really made it so the same sites pop up on top for certain classes of queries. (for example Reddit will be on top for product reviews alot). These sites operate on ad revenue so their incentive is to block. Perplexity does whatever they can in the game of sidestepping the sites' wishes. They are a bad actor.
EDIT: I should also add that Google, Bing, and others, always obey robots.txt and they are good netizens. They have enough scale and maturity to patiently crawl a site. I wholeheartedly agree that if an independent site is also a good netizen, they should not be blocked. If Perplexity is not obeying robots.txt and they are impatient, they should absolutely be blocked.