The term ‘Grid Computing’ is relatively new and means a lot of different things to a lot of different people[19]. It has been used as a buzzword for any new technology to do with computing, especially computer networking, and therefore it has been over-hyped as the solution to just about every computing problem. One of the goals of this paper is to give a clear definition of what Grid Computing is and why it is required. Grid Computing, or Network Computing, is intended to provide computational power that is accessible in the same way that electricity is available from the electricity grid - you simply plug into it and do not need to worry about where the power is coming from or how it got there. The idea of Grid Computing is the same - if more computing power is required, spare cycles on other computers are used. This means that super-computer type power is accessible without the huge costs of super-computing, and that CPU cycles that would otherwise be wasted are put to good use. In fact, one of the major researchers into Grid Computing, Ian Foster from the University of Chicago says “grids are above all a mechanism for sharing resources”, [13]. This means primarily sharing CPU time but also other things such as data files. Although this description sounds simple there are a number of problems with creating Grid systems - how do you access computers with different operating systems, how do you find those computers to access and how do you make sure that you can trust others to run code on your machine? In fact, how do you encourage people to let others run code on their machines in the first place? These questions, and many others, need to be answered for Grid Computing to succeed and they are also discussed in this paper. Grid Computing is no longer just a concept to be discussed but is something that is actually used every day. There are many Grids around the world, and many researchers investigating how to do Grid Computing better. These current Grids and the some of the current Grid research topics are also discussed in this report. There is also significant potential for Grid Computing to be used at the University of Canterbury. There are several projects which are very well suited to Grid Computing and it is likely that others would emerge were a Grid system available. The potential for Grid Computing and some of the tools that could be used for this are discussed below as well. The layout of this paper is as follows: Section 2 discusses why Grid Computing is needed at all. Section 3 discusses what makes up a Grid system, and Section 4 discusses some current Grids and Grid technologies. Section 5 discusses some of the current issues that need to be addressed in Grid Computing, Section 6 1 discusses the possibility of Grid Computing at the University of Canterbury, and finally section 7 concludes.