An anytime algorithm is an iterative procedure that can be interrupted at any time and return a valid, progressively improving solution, with quality that increases monotonically (often non-decreasingly) as more computation time is allocated. Anytime algorithms are designed for settings with bounded or uncertain resources (time, memory, energy), where the system must trade solution quality against deliberation cost. Two formal components characterize them: a performance profile that maps allotted computation to expected solution quality, and a stopping/monitoring policy that decides when to terminate. Under a fixed resource budget, the algorithm must terminate gracefully, returning the best solution found so far rather than failing, which is the property that motivates imposing explicit budgets on search procedures.