Association Rule Mining (ARM) is one of the well know and most researched technique of data mining. There are so many ARM algorithms have been designed that their counting is a large number. In this paper we have surveyed the various ARM algorithms in four computing environments. The considered computing environments are sequential computing, parallel and distributed computing, grid computing and cloud computing. With the emergence of new computing paradigm, ARM algorithms have been designed by many researchers to improve the efficiency by utilizing the new paradigm. This paper represents the journey of ARM algorithms started from sequential algorithms, and through parallel and distributed, and grid based algorithms to the current state-of-the-art, along with the motives for adopting new machinery.