It contains a number of films and exhibits exploring Welsh history as well as spaces to function as venues for public debate and assembly-sponsored events.
Lord Elis Thomas said: "This has now become a public space where people can express their views about what's happens over the street in the National Assembly building itself."
One exhibition showcases artefacts including the original binnacle (the stand housing the ship's compass) from Scott of the Antarctic's ship the Terra Nova, and the Pennal Letter sent by Prince of Wales Owain Glyndwr to Charles VI of France in 1406.
Another features an audio-visual display of Welsh heroes - people who have made significant contributions to Wales' cultural and political identity.
The Pierhead houses the binnacle from Captain Scott's SS Terra Nova.
These range from Prime Minister David Lloyd George through fashion designer Laura Ashley to the late rugby player and broadcaster Ray Gravell, and many more besides.
Lord Elis Thomas said: "[The concept is] changeable video heroes, so that it's not one version of Welsh history but all sorts of versions that people can enjoy."
Films and exhibits explore the history of Cardiff Bay from the Neolithic era onwards and show how iron ore and coal exports made Cardiff one of the busiest ports in the world.
They describe the impact of the coming of railways from 1841, which meant goods could be transported as far in an hour as they would have been in a month using the canal system.
They also illustrate how, following the crisis of a steep drop in demand for coal in the 1920s, and its decline as a port for container ships from the 1950s, Cardiff Bay entered a difficult period, ending with its regeneration at the century's close.
Visitors can listen to audio accounts of individuals' experiences of Cardiff Bay.
One exhibit emphasises the importance of north Wales' resources to the iconic building.
The Pierhead is constructed from clay-based terracotta supplied at the end of the nineteenth century by JC Edwards & Co of Acrefair near Ruabon in Wrexham - once described as one of the most successful producers of terracotta in the world.
More than 2,000 people in the Wrexham area were involved in that trade, with Ruabon known as "Terracottapolis".
The Pierhead building was designed by Welsh architect William Frame (1848-1906), who also worked on the refurbishment of Cardiff Castle and Castell Coch.
The re-opened building isn't just about the past. It provides space for present-day organisations to hold debates and events.
It also features a "futures gallery" in which people can highlight issues of concern to their communities, in the hope that assembly members situated just across from the Pierhead will act upon them.
There is an emphasis on interactivity throughout, with facilities for visitors to record their impressions of the building - and see what they've written in electric lights.
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