Luxembourg's a small country: even the "IKEA Luxembourg" is not in Luxembourg, but just across the border in Belgium! That said, travel within the Schengen Area is relatively straightforward, but some things are to be taken into account.
NB: This is not a substitute for legal advice; always check the rules before you travel!
- You must always have valid documents to cross an internal (Schengen) border. If you're an EU/EEA/Swiss citizen, your national ID card (if it doesn't have a "not valid to cross the border" endorsement) or valid passport is sufficient; if you're not, you must have a valid passport; if you have a residence card (titre de séjour or carte de séjour), you must carry this as well. (A residence card alone is not valid to cross an internal Schengen border!) There can be spot/random checks at the internal Schengen borders, especially when travelling by plane.
- If you're not an EU/EEA/Swiss citizen not subject to a visa requirement: For the first 90 days of your stay, counting from the date of your entry stamp, you may travel freely within the Schengen Area (you'll be seen as a "tourist" in the other Schengen countries, even if you have a residence permit for Luxembourg). After those ninety days, however, you must have a valid residence permit in hand to travel to other Schengen countries.
- If you're not an EU/EEA/Swiss citizen, require a visa, and have a C visa: You can travel within the validity of the C visa to any other Schegen country if your visa reads Valable pour États Schengen (or something similar). A minus sign in front of country abbreviations means your visa is not valid in those countries, while a list of countries means that your visa is only valid in those countries.
- If you're not an EU/EEA/Swiss citizen, require a visa, and have a D visa: You can travel within the validity of the D visa to any other Schengen country, provided you do not stay more than 90 days in a 6-month period in any of the other Schengen countries. (A D visa acts like a C visa in all other Schengen countries.) Once the D-visa expires, however, you must have a valid residence card to travel within the Schengen area.
- If you're not an EU/EEA/Swiss citizen and have a Luxembourgish residence permit: A valid Luxembourgish residence permit acts as a substitute Schengen visa for a combined stay up to 90 days in a 180-day period in other Schengen countries. Mobility rules for holders of student (étudiant) or researcher (chercheur) residence permit can allow for a continuous stay of 180 days in other Schengen countries (except Denmark and the EFTA countries) without a separate long-stay visa, but subject to a prior notification procedure.
Special Cases
Cyprus While an EU (and eurozone) country, Cyprus is
not yet in the Schengen Area. However, valid Schengen visas and valid residence permits are valid for travel to Cyprus unless you are a Turkish or Azerbaijani passport holder.
Ireland While an EU (and eurozone) country, Ireland is
not in the Schengen Area and
separate entry documents may be required for travel to and/or through Ireland if you are not an EU/EEA/Swiss citizen. There is an Irish Embassy in Luxembourg if you need to apply for a visa.
EFTA Norway, Switzerland, Iceland, and Liechtenstein are
not EU countries, though they are in the Schengen area: this means that certain EU rules regarding long-stay visas and/or research mobility do not apply and there are customs controls for travel to and from those countries. Additionally, the standard European Health Insurance Card (EHIC) may not be valid in EFTA countries unless you are also an EU/EEA/Swiss citizen; make sure to check your insurance before you travel.
Denmark While Denmark is a Schengen Area member state, some provisions of EU law do not apply to non-EU citizens (EHIC validity, the validity of long-term visas, and mobility exchange rules). However, citizens of Australia, New Zealand, Canada, Chile, Israel, Japan, Panama, South Korea, Uruguay, and the United States can stay for up to 90 days in Denmark without reference to the time spent in other Schengen Area countries.
The United Kingdom As the UK is not an EU country, a separate visa policy is in force for travel to/from the UK, and EU visas or residence permit documents are generally not valid (except for transit). Unless you are an Irish citizen, you must have a valid passport and either
an Electronic Travel Authorisation or a full visa to travel to the UK.