There are a lot of specific parking places for taxis in Luxembourg. You can find such in front of Luxembourg Central Station, Rue Notre-Dame behind the Cathedral in Luxembourg-center, at the Glacis car park (Allée Scheffer) for example. Of course, you can hail a taxi from the street as long as it's 50 metres away from the parking spot. The taxi fares are different and not regulated, which means that every carrier might have different prices. Make sure to choose one with visible prices since the drivers are not allowed to ask you for more than displayed. It is known that Luxembourg taxis are one of the most expensive in the world.