The shape of Lishu characters are identical to modern Chinese characters, Furthermore, characters were standardized to remove regional variations, and these standard characters are for the most part the same characters written in the present. Therefore, it can be said that Chinese writing reached its maturity at this time (until the 20th century).
Evolution of Chinese writing after Lishu is a trend of increasing cursive scripts. These scripts are the ones used in calligraphy.
The most important change in Chinese writing since the standardization in the Qin dynasty occurred in the middle of the 20th century. In 1949, the People's Republic of China (PRC) introduced simplified characters (jiantizi) to replace the traditional Kaishu characters. In addition to PRC, Singapore also adopted this script. However, other Chinese-speaking places such as Taiwan, Hong Kong, and various Chinese communities in Southeast Asia and the Americas rejected this new system and continued to use the traditional script. Tradition runs deep in Chinese culture, and the fact that the simplified script carried politic issues, certainly did not help its wider acceptance.
Not all characters were given a new simplified form, as these unsimplified characters were already very "simple" and involve very few strokes. Some simplified characters were in fact official recognition of widely-used colloquial variants of traditional characters.
The Origin of Chinese Writing
The precursor to Chinese writing, though, is still poorly understood. In many pots, jades, and bronzes ranging from the late third millenium BC to as late as Shang and Chou dynasties, bird and sun motifs appear together, often joined, and possibly can be read as yang niao, or "sun birds", the name of a local eastern Yi group which had settled in the Lower Yangtze valley. This could be an example of the a precursor to Chinese writing.
Current theories and evidence pinpoints the first emergence of Chinese writing in the East Coasts between the Late Neolithic and the early Bronze (aka dynastic) times. The culture which occupied this area was characterized by a high degree of social organization, particularly in pottery production (parts of their pots were made separately and later assembled together). It could be that this "standardization" led to the necessity of recording dimension of pots as well as the number of pots produced, thus the impetus to create a systematic way of recording number and objects.
The Earliest Chinese Writing
Whatever the obscure initial phase of written Chinese was, its appearance during the Shang already gives sign of a very complex system. Phoneticism was widespread in the form of the rebus principle, which means many words with the same sound can be, and were, written with the same sign. A most common example in English is to use pictures of a bee and a leaf to write belief. This leads to ambiguity in written text (if you're a Chinese speaker, think of the confusion that would be generated if you write "horse head" and "harbor" the same).
To alleviate the ambiguity, scribes started to attached additional symbols to clarify the meaning. In modern Chinese studies these signs are called "radicals". Also, the phonetic "spelling" of words was standardized, in that while previously two signs represented the same sound, only one of them continued to be used while the other became obsolete.
Sometimes new signs were created by combining two signs and the meaning of these two signs. Thus, the sign for "bright" is a combination of signs for "sun" and "moon".
Because of changes in the language such as sound changes, the introduction of tones, and branching into new languages, the phonetic part of many modern characters no longer provide any clue on how to pronounce the characters. Therefore learning Chinese becomes a matter of memorizing forms with only an occasional help. It is because of this that the Chinese writing system is misleadingly labeled as "ideographic", because, as many would argue, every sign stands for an idea. This is untrue and pretty absurd, as a writing system records a language, not replicates ideas, emotions, or other mental states. In essence, Chinese is "logographic", that is, its symbols write out words.
I recommend going to the website and touring around it. There are lots of interesting things to see. If you go to the page that I got this article from you can see a representative chart of the evolution of Chinese script.
Lo, Lawrence. 2005. "Chinese". Ancient Scripts. Available online: http://www.ancientscripts.com/chinese.html