Anytime Heuristic Search, formalized by Hansen and Zhou (JAIR, 2007), converts best-first heuristic search such as A* into an anytime algorithm. The procedure uses weighted heuristic search with weight $w \geq 1$ on the heuristic ($f(n) = g(n) + w \cdot h(n)$) to find an approximate solution quickly, then continues the weighted search to discover improved solutions and to tighten an upper bound on the suboptimality of the current best solution. The result is a sequence of monotonically improving solutions and a shrinking suboptimality gap that converges to an optimal solution if search is allowed to complete. The algorithm gives a flexible quality/time tradeoff under explicit resource budgets and is the canonical reference for budgeted best-first traversal motivated by anytime search.