Undergraduate (international first-year): You generally need your application (ApplySUNY/Common App/Coalition), academic records/transcripts (with English translations if not originally in English), and materials used in holistic review (which can include test scores, an essay, and recommendations). You may also need to submit proof of English proficiency through an accepted test (unless exempt), and UB specifies that official scores must be sent from the testing agency after initial review.
Graduate: Requirements are decentralized by department, but UB commonly requires an online application, transcripts from every college/university attended (often unofficial for review, with official transcripts required after admission), letters of recommendation, and any required test scores (GRE/GMAT/etc. only if your program requires them). Many programs also ask for a statement of purpose and a resume/CV. International graduate admits also typically provide visa-related documents (for example, passport ID page and financial documentation) during the acceptance process.