Austrians
Historically, Austrians were regarded as ethnic Germans and viewed themselves as such. Austria was part of the Holy Roman Empire and the German Confederation until the Austro-Prussian war in 1866 which resulted in Prussia expelling Austria from the Confederation. Thus, when Germany was founded as a nation-state in 1871, Austria was not a part of it. In 1867, Austria was reformed into the Austro-Hungarian Empire. After the collapse of the Austro-Hungarian Empire in 1918 at the end of World War I, Austria was reduced to a rump state and adopted and briefly used the name the Republic of German-Austria ("Republik Deutschösterreich") in an attempt for union with the Republic of Germany, but was forbidden due to the Treaty of Saint-Germain-en-Laye (1919). The First Austrian Republic was founded in 1919. The Third Reich annexed Austria with the "Anschluss" in 1938.
Austria–Switzerland border
The current border is a product of the creation of the Helvetic Republic in 1798. During the 19th century it was part of the western border of the Austrian Empire and later Austria-Hungary, and in the 20th century of the First Austrian Republic, the Federal State of Austria, Nazi Germany and Allied-occupied Austria, and eventually of modern Austria since its formation in 1955. 
Liechtenstein was created as an independent principality under the Peace of Pressburg (1805), although it remained nominally a member of the Confederation of the Rhine until 1866).