The most important part of moving to the EU is your ability to live and work legally within its borders. All European Union member states shares customs and immigrations, allowing for the free movement of its citizens across all nations, but the visa application process for all non-EU citizens is done directly with the country which you are moving to and the requirements differ for each one. Be sure to look at the requirements of the specific EU country you are relocating to.
Is the country you are relocating to in the Schengen area or The EU? The two terms are sometimes used interchangeably but not all European Union Countries are in the Schengen Area and not all Schengen Area countries are in the European Union so it is important to know difference between the two. This information may be important when traveling to your new country of residence if you have a layover in a country where you require a transfer visa (such as the UK which is an EU country but not part of the Schengen area) or when considering leisure travel plans.