As someone who is interested in the history of botany, I'm well aware of the very important invention of binomial nomenclature by Linnaeus and his role in botany at large, which includes his plant classification system, which he published in Systema Naturae in 1735. The history around this important botanist and his system is more or less well known to the community of historians of science. Since plant taxonomy almost certainly didn't stand still in the following centuries and probably still is an important part of plant biology even today, I was wondering what this sub knows about plant classification systems after Linnaeus inventions.
I would also be interested in books or other publications (preferably recent ones) about this topic.
I can't tell you how the biologic classification changed, but I can tell you why it did. The microscope had been around for awhile, but only around 1830 did it become reasonably priced and available to a wider variation of scientists or enthousiasts. Despite some early knowledge of microscopic organisms, a lot of botanic knowledge was still very "superficial". It was mostly based on observations and experience without the aid of a microscope. When the Phytophthora Infestans struck the potato harvest at a time when it seemed like the great famines of old were long gone, it caused a panic in Central Europe. Though the effects in continental Europe weren't as dramatic as they were in Ireland, they were still far-reaching. Not only did it destroy big portions of the harvest in 1845, it also severely diminshed the harvest of subsequent years. As a result, there was an increased attention and availability of funds for research regarding plant biology. Both the breeding of plants and the study on a microscopic level received a lot of attention. Around this period in time, we see the emergence of many botanic gardens and research institutes. It's not a coincidence that Gregor Mendel developped his theories around this time and based them on plant research. Doing research on a microscopic level quickly showed that Linnaeus his classifications weren't sufficient nor entirely correct. For example the potato famine itself was caused by a previously unknown type of organism, the Phytophthora Infestans. It's an omycete which is a bit like a fungus.
As for the "how", it could help to ask people in /r/AskScience as /u/Searocksandtrees suggested. I can only advise you some works I used to do research, but I'm not sure if it's what you are looking for seeing as it was only partially overlapping with my subject :
STEVENS, Neil E., ‘Plant Pathology in the Penultimate Century’, in: Isis volume 21.
CITTADINO, Eugene, ‘Botany’, in: Bowler, Peter J., Pickstone, John V., The Cambridge History of Science volume 6.
hi.. it might be worth x-posting this question to /r/AskScience (Biology category)