It's not as standardised as you might think. Spelling varies considerably from country to country, and even within a single country there is variability both regionally and on a person-to-person level. There is no official standard of English in America, for example. While most dictionaries for Americans will agree, this consensus is a matter of convention and not the result of any sort of national government oversight.
There are dictionaries which have been elevated in status among speakers of a certain dialect. In Australia the Macquarie Dictionary is often considered the standard of Australian English spelling and usage, though like all dictionaries it's describing use and not telling people how things should be. Webster's has long been considered an ideal for American spelling and usage. Canada has the the Canadian Oxford Dictionary. These three dictionaries will not agree on a large number of spellings.
In each of these countries there have been proposals for spelling reform, but these are only as good as how much people are willing to adopt and conform to them. In Australia this was met with some success in the 1970s, and Macquarie is reflective of this. Some efforts were less successful, such as America's proposed simplified spelling which was backed by President Roosevelt and Andrew Carnegie. Noah Webster's efforts were a little more successful and were propagated through his dictionary. Someone else might be able to speak more on specific efforts in Canada which I'm not as aware of.
Spelling reform is a pretty major issue in most large languages, and efforts have been made for centuries to create a more uniform standard within a given variety (or country), but not on a larger "all of English" scale. What this means is that if you take a point in the past couple hundred years up to today, the different standardisations you're seeing are actually pushing the different varieties' spelling systems further apart. What conventions there are that might shared between varieties of English are themselves often just the luck of the draw, being the chosen spelling out of a variety of possible spellings that were once in use. You can see this if you look at older texts, where a single word might be spelled two different ways even in a single paragraph, and definitely different between two different authors.
If there are future spelling reforms in American English, it will be done to represent the American pronunciation more phonemically, and not take into account the way words are pronounced in other Englishes. This means that over time, if the trend continues, you could potentially see a split where someone in the US could actually have trouble reading something written in England. We're obviously not there, but it's not impossible.
As a bonus, see this thread for yet one more instance of a word's spelling changing (without some external push to make it happen) where "shew" fell out of use in favour of "show" with "show" simply being more representative of the more current and more widely used pronunciation of the word.
If we take British English into account, the influence of the printing press is a huge factor if the modern spelling, but it's far from rendering it fully standardised. William Caxton introduced it to the UK in 1476 and when starting to print in English, he used his relatively conservative London dialect. This lead to printing conventions of using that one variety of English to make the process easier and its popularity spread. Apparently, his dialect was one of few that retained the "right" spelling and pronunciation over "rite", which is why that is still the practiced spelling.
Later during the Early modern English period, there were several movements to either "fix" the language as it was or to perform various spelling reforms. For example John Hart wanted a more phonetic English alphabet in line with the Classical languages. This included removing any silent/superfluous letters. He did succeed in introducing j and i as separate letters and u and v as a vowel and a consonant inherently rather than depending on their location in a word. Another was Richard Mulcaster, whose suggested standardisations were popular and regulated the use of the final e to show the quality of the preceding vowel. There were other movements as well, such as those changing the spelling of words to make them sound more Latinate despite them not having that etymology (debt, island, admirable).
So while there certainly were movements to try to standardise the spelling of English, there was never one overarching and successful type that settled the issue for good. Variations of spelling within one person's language use was still very common in the Early modern English period, including how to spell his or her own name.