'Randomness in the Limit' uses ultraproducts to convert questions about counting configurations in finite graphs into problems in probability and measure theory, where powerful tools become available. Along the way, it develops a decomposition of 'structure' and 'randomness' central to modern extremal combinatorics, culminating in a complete proof of Szemerédi's Theorem. This self-contained introduction surveys every major framework for taking limits of dense graphs – ultraproducts, graphons, and flag algebras – explaining how to translate between them. It systematically shows how to interpret infinitary theorems in concrete, finitary terms, revealing the power of infinite perspective. Logical tools are introduced only when needed and are motivated by the specific problems they solve, making the subject accessible to readers without prior expertise in logic. This is an ideal text for graduate students and researchers working in probabilistic and extremal combinatorics, model theory, and logic.