There are quite literally thousands of Forex Robots, on the market at the moment, they come in all shapes and sizes and can use any type of strategy to initiate and exit trades. Typically they use some type of mechanical or neural networking algorithm to perform this task. Whether it be in the form of a technical analysis indicator such as MACD or simply using a price level to enter and exit trades.

I have identified 5 broad types  of Robots and give a general description of the type of logic and functions involved in these types of robots, without getting too scientific and entering the realm of rocket science. I am sure that there are many other types of Robots using a host of other methodologies, most of which are so called "black boxes" where the exact methods are not made public and cannot easily be reverse engineered.

1. Trend Trading Forex Robots:These robots look to identify an existing trend or change in trend or counter trend, by using any number of mechanical indicators or neural networking algorithms to trigger trade entry and or exit. This probably accounts for the vast majority of forex robots. If you can successfully identify a trend and exit at an appropriate time then you may well have the beginnings of a trading system.
2. Breakout Trading Forex Robots: Usually look to trade at the start of a trading session, with the London opening session usually being the most productive to trade. This type of robot looks to trigger a trade once the price breaks out of the range of the previous Asian trading session which is usually typified by lower trading volumes and shorter price ranges.
3. Grid Trading Robots:  So called grid traders first became popular amongst automated forex traders 4-5 years ago and rapidly developed a hard core following amongst automated forex traders. They basically rely on price action rather than any technical analysis indicators, and set up a series of closely separated trades or "grid" on either side, above and below the current price. The theory being that no matter what happens with price the robot will collect relatively small but numerous trades. Usually there are large volumes of trades open at any one time so that factors such as margin and money management can become critical after large moves in price action. Grid trading is still a popular form of trading in retail forex, especially with the advent of Metatrader and micro accounts.
4. Scalping/Range Trading: Usually look to trade the less volatile currency pairs, such as eurchf, eurgbp during the less volatile (Asian) session. usually typified by a large volume of trades, whilst looking for relatively small and frequent gains. This is also a very popular method for Forex Robots but probably best to check with your broker to see if they accept this type of trading strategy.
5. News Trading Robots: Various methods are used to trade the fundamental news events, some are triggered by the specific news data release, other use some form of pattern or price action to initiate a trade. These types of robots are extremely time sensative because of the relatively short period of time and large movements. Your brokers trade execution and slippage can be critical. This form of trading seems to increase and decrease in popularity with the market volatility as the effect of fundamental news releases changes.