An algorithm is a mathematical formula that maps a set of steps for solving problems. For most consumers, it is the tool that calculates what we might be interested in finding on Google or Amazon. In financial markets they do all the buying and selling of assets, be it shares, derivatives or currencies. With a few exceptions, it is almost impossible to trade on an exchange without one. 
Algorithms have become a common feature of trading. Essentially software programs, they decide when, how and where to trade certain financial instruments without the need for any human intervention. 
High-frequency traders have been at the cutting edge of development in recent years driving trading speeds across continents down to milliseconds. They have sifted through huge quantities of data thrown up by the fragmentation of markets and looked for patterns to exploit.
Often HFT has focused on inefficiencies in the speed and reliability of the technology, the market plumbing. Some strategies have focused on a single asset class, such as stocks. Others have been more imaginative, looking at ways to arbitrage unusual securities across asset classes. Some have gone even further, with strategies containing complex mathematics and physics, and have borrowed from diverse industries such as defence and voice recognition. These investors are relatively few.
Regulators are worried about algorithms. Around the world, they are concerned about potential destabilising effects and damage to the integrity of the markets. But they are in a dilemma. While regulators want a stable, fair market, they also accept that innovation and efficiency is an important part of its development. Many are examining how to best oversee the market and have even considered examining the algorithm’s code. But they have been dissuaded by practical considerations such as understanding it and their potential liability if an algorithm later turns rogue. So far Germany has gone furthest, demanding HFT traders are licensed.