After the introduction of MiFID (Markets in Financial Instruments Directive) in Europe in November, 2007, the erstwhile ATS have been renamed as Multilateral Trading Facilities (MTF), and these are governed like traditional exchanges, also called as regulated markets, under the provisions of MiFID.
This system is, just like a regulated market, multilateral. Multilateral means that multiple parties can input their selling and buying intentions into the system and a transaction is established between these parties when intentions match. The third trading system introduced by MiFID is internalisation, which is bilateral. This means that the counterparty in a transaction is always the investment firm.
Note that MTF's can be quite different in appearance. They can appear as regulated markets-'light' such as Alternext, but also as a alternative trading platform for regulated market securities, such as Chi-X and Turquoise.