In competitive programming, problems involving large integers can easily lead to overflow errors if you're not careful. Many programming languages like Python handle large integers natively, while others like C++ or Java require special libraries or data types like BigInteger. In problems where the results can grow extremely large, modular arithmetic is often used to keep the numbers manageable, especially when the result needs to be computed modulo a large prime number. Efficiently managing large integers is crucial in problems involving combinatorics, cryptography, or number theory.