An ANT is a mobile agent that is capable of solving various kinds of routing and congestion problems in computer networking by continuously modifying routing tables in respond to congestion. In a distributed problem solving paradigm, a society of ANTS (each contributing some information) collaborate to solve a larger problem. In recent years, Ant-based algorithms were used to solve classical routing problems such as: Travelling Salesman Problem, Vehicle Routing Problem, Quadratic Assignment Problem, connection-oriented/connectionless routing, sequential ordering, graph coloring and shortest common supcrscqucncc. By introducing the general idea of Ant-based algorithms with a focus on Ant Colony Optimization (ACO) and their mathematical models, this paper brings together a collection of ACO algorithms discussed their features, strength and weaknesses.