Two firms, not one
Citadel is a multi-strategy hedge fund. Citadel Securities is a market maker. They are separate companies, they do different things, and they run separate hiring pipelines with their own recruiters, their own timelines, and their own emphases. Both publish their own account of how they interview for quantitative research, and both are linked in the sources below - read the one for the entity you are actually applying to, because a Citadel Securities process is not a Citadel process.
This split is the most common avoidable mistake in preparing for either. It is also why generic "Citadel interview" advice found online is often subtly aimed at the wrong firm.
What the processes have in common
Both sides publish guides for candidates rather than leaving the process opaque, which is worth taking advantage of - the primary sources are short and specific. Across both, candidates commonly report a screen followed by technical rounds combining probability and statistics with coding, and a final stage weighted toward depth in your own past work: expect to defend a project or a piece of research in detail rather than only to solve set-piece puzzles.
Prior work is genuinely load-bearing here in a way it is not everywhere. Candidates consistently describe being pressed on the specifics of what they personally did on a project, so a thin claim on someone else's work is a poor bet.
What to prepare
Probability and statistics, precisely rather than broadly. The reported emphasis is on getting conditional-probability and estimator reasoning exactly right, not on covering more topics.
Your own research, in detail. Be able to say what you did, why you chose it over the alternative, and what you would do differently. This is the part candidates most often under-prepare.
Coding that runs. For engineering and quant-developer tracks the coding rounds are reported to be substantive rather than a formality.
Formats shift, and both firms update their own pages, so treat any specific stage count you read anywhere - including here - as a candidate report rather than a guarantee, and the linked primary sources as authoritative.
Practise the same formats
The question sets below are ours, written in the formats these processes are reported to use. They are not either firm's questions, and nothing here reproduces any part of any assessment.