By Plane

Antwerp has a small airport, located close to the city center. A couple of airlines maintain connections to a handful of airports, including London City, Manchester and Liverpool.
For flight schedules, check out the airport's website.
The VLM airline has its base in Antwerp, check out their website here.

Belgium's national airport is about 40km from Antwerp's city center. Flight schedules can be found on the airport's website.

The airport can be reached either by train or bus.

The most convenient is the SN Brussels Airlines airpoirt shuttle which departs every hour from the bus stop on the De Keyserlei street, near the Central Station (across the 'Century Center' shopping center). Timetables and info can be found here.

There is no direct train between Antwerp and the Zaventem airport (yet - it is planned for 2010). You have to transfer at the north station in Brussels. You can use the railway route planner from the national railways - use 'Brussels airport' for the airport and 'Antwerpen Centraal' for the central station in Antwerp.

By Train

A direct high speed train (Thalys) brings you in less than two hours from the Gare du Nord in Paris to Antwerp. The train stops at the Antwerp central station (and not anymore at the Berchem station).
More info can be found on the Thalys website. Mind you, Antwerp is sometimes referred to as 'Anvers' (French for Antwerp) on this website...

The Eurostar, a high speed train, connects London Waterloo Station to Brussels South Station. From there, you can take a regular train directly to Antwerp Central Station.
For more info, check out the Eurostar website

The high speed train route between Antwerp and Paris now stops at Antwerp's central station (and not anymore at the Antwerp berchem station). You can also take a regular intercity train, which connects the Amsterdam Central Station to the Antwerp Central Station in about 2 hrs. The high speed train is currently not much faster but you can reserve seats. The trains also stop at the Schiphol National Airport. For schedules, see here.

The Thalys high speed train connects Antwerp to several cities. For connections to other cities, check out the railway route planner of the NMBS, the local railway.