Installed in 1410, the world's oldest astronomical clock, still in operation, is called the Orloj and is in Prague, capital of the Czech Republic.
The Orloj is mounted on the southern wall of the Old Town Hall in the Old Town Square. The clock mechanism itself has three main components:
1. The astronomical dial, representing the position of the Sun and Moon in the sky and displaying various astronomical details
2. Statues of various Catholic saints stand on either side of the clock; "The Walk of the Apostles", a clockwork hourly show of figures of the Apostles and other moving sculptures, notably a figure of Death (represented by a skeleton) striking the time.
3. A calendar dial with medallions representing the months.
The oldest part of the Orloj, the mechanical clock and astronomical dial, dates back to 1410 when it was made by clockmaker Mikuláš of Kadaň and Jan Šindel. This makes it 608 years old, and give or take the odd fire, mechanical failure and Nazi invasion it has been ticking ever since.
I've actually seen the clock in person when I was in Prague, it was beautiful, a wonderful marriage between engineering and art.
Further Info: https://en.wikipedia.org/wiki/Prague_astronomical_clock