If you have come across Korean historical dramas, chances are you may have observed that the writing system used in enacting historical periods are dominated by Chinese characters.
In Korean, these Chinese characters are known as Hanja (漢字 / 한자).
The older the historical period, the more Chinese characters you will see. For example, in the historical Korean drama The Great Queen Seondeok (善德女王 / 선덕여엉) set in the Silla Dynasty around the year 500–700s, you can observe that there was absolutely no Korean alphabets used, because they simply didn't exist at the time.
The modern Korean alphabets in use today were developed in the 1440s under the reign of Sejong the Great (세종대엉), the fourth King of Korea's Joseon Dynasty.
These alphabets are known as Hangeul (한글).
That is why you would only be able to notice instances of Korean alphabets being used in historical dramas set in periods after the 1440s, such as in Dae Jang Geum (大長今 / 대장금), which was set in the 1600s.
Hanja was prominent throughout the Korean monarchy. This was because being able to read Chinese characters at those times reflect aristocratism and high-class education. The Korean society at that time were divided into class systems, and often low-class members of the society such as slaves were considered illiterate as they have no knowledge of Chinese characters. Many, however, learned how to read and write the simple set of Hangeul after its conception.
Of course, this does not mean that Hangeul was abandoned by those belonging to the royalty and nobility society members for the sake of supremacy. The effectiveness of Hangeul in the Korean language has in fact contributed to the use of mixed script between Hangeul and Hanja in a number of historical documents after the 1440s.
The widespread use of Hanja remained well until the 1900s, when Korea came under the Japanese rule. This is a period where the Korean monarchy and class system collapsed. Education were hardly accessible and as a result, the literacy rate was at an all-time low. Additionally, with the aftermath of the war resulting in the split of Korea into North Korea and South Korea, both countries began reducing Chinese linguistic influences, and moved towards using the Korean alphabets to its full extent.
In the late 1940s, North Korea abolished the use of Hanja in favor of Hangeul in its writing system. The South sought to increase literacy rates during this period, with social groups advocating for the use of Hangeul exclusively in its writing system, but this did not go through as official documents were still written in mixed script. It was only until the 1970s that South Korea began using Hangeul exclusively in official documents, newspapers, and other media channels. Hanja was also removed from school textbooks. Today, all Korean communication uses Hangeul, praised by many linguists as one of the most effective writing system ever developed.