While I was in a London for a few days in July 2015 I visited the Magna Carta: Law, Liberty and Legacy exhibition at the British Library, which was put on to mark the 800th anniversary of the original issue of the charter. The items displayed in the exhibition were mostly written documents (as you might expect in a library) although there were also some other things, including paintings and examples of seals. There were also several short films each of which had someone talking about a particular aspect of the charter & its legacy. The talking heads were a variety of historians, lawyers and politicians. I did like these, they added quite a bit to the exhibition, but they also broke up the flow a bit - there wasn't always enough space for people to walk past those who were standing and watching them, so at times the galleries felt clogged up.
The first section of the exhibition put Magna Carta into its original historical context. There were some examples of charters issued by previous kings (such as one by Henry I), and some contemporary accounts of King John. One of these was written by Matthew Paris, who really didn't much approve of John - something he wrote after John's death included the quote: "Hell foul as it is, is made fouler still by presence of John"! In this section they also displayed some earlier drafts of the charter, made as it was being negotiated at Runnymead. And they had several examples of seals, including the one used by John to seal the Magna Carta. Almost immediately after the Magna Carta was issued John repealed it - asking the Pope to declare it invalid in a Papal Bull (which was there to see in the exhibition). When he unexpectedly died during the ensuing civil war his young son Henry came to the throne at the age of 9. He began a period of using reissuing the Magna Carta as a means of legitimising the authority of the King which continued over the next century or so.
They had a rather neat animated graphic in the exhibition which showed the various clauses being weeded out over time until only the last few more general ones remained. This covered up until the modern day, despite it's placement at this point in the exhibition - I think because after this the exhibition moved on to looking at the legacy rather than the actual thing itself. The common theme tying together the rest of the exhibition was that "Magna Carta" came to represent more as an idea and a totem than was actually present in the original document.
After the 13th Century the importance of the Magna Carta faded - to the extent that when Shakespeare wrote his play about King John in the 16th Century he didn't even reference the document. There was a revival of interest in it in the 17th Century which is the beginning of the modern prominence of the document. It was used to justify rebellion against a tyrant King during the run up to the Civil War and subsequently used against Parliament when they were felt to be becoming tyrants.
Magna Carta has become extremely important both in US culture and US law. The Declaration of Independence draws on the charter and uses language that directly references it. Even before that the laws of the early colonies were based on Magna Carta. It's still important in the US legal tradition today - one of the talking head videos was explaining that it has been used as part of the legal argument against the incarceration of people in Guantanamo Bay.
During the 18th & 19th Centuries radicals within the UK continue to use Magna Carta when challenging the government, for instance the Chartists write a new revised version suitable for their times (and agenda). Magna Carta was generally not applicable in the British Empire, and one of the things that the 20th Century sees is the the newly independent ex-colony states issuing documents to grant these rights to their citizens. And there's a tendency for grants of legal rights to be referred to as the Something Magna Carta (i.e. the Maori Magna Carta) even tho the content of the documents is very far from the content of the original Magna Carta (which is really quite specific and parochial in scope despite the later reputation). More recently it has also been invoked by Nelson Mandela and by Aung San Suu Kyi. In contrast to Shakespeare's day the Magna Carta is now also likely to show up in popular culture. The penultimate section of the exhibition displayed several examples of this - including thoroughly anacronistic representations of King John signing the charter!
The exhibition then finished with the showpieces - two original copies of the Magna Carta. One of these was from Canterbury and had been very damaged, whereas the other one was in much better condition. Of course, it was in Latin (and abbreviated wherever possible) so even being able to see the text didn't mean I could read it!
It was an interesting exhibition - although I think I was more interested in the beginning sections about the medieval history (and the very end) rather than the bits about the legacy. I was interested enough overall to buy the book tho! :)