We now have 50 years of accumulation in the study of Korean art history. The number of students and scholars doing research in the university has also increased greatly. Researches are actively going on and noticeable achievements are being made in the field. But there is still a way to go until the standard of the study of Korean art history reaches one of the top levels in the world. More enhanced understanding and in-depth discussion is required in the tasks and methodology of the study of Korean art history and in the connoisseurship and art historical point of view. In this article, I would like to examine the accomplishments so far and make a suggestion for the future direction. The Art History circle today has a lot of tasks to fulfill. In this chapter, discussion will be confined to fundamental and theoretical aspects to evade redundancy. We will talk about the tasks in each field. The tasks pending in the study of the History of sculpture may be listed differently according to scholars. First. the most important task is to eliminate any misunderstanding that might arise due to a lack of understanding in the basic concepts such as 'form', 'style' and 'iconology'. Second, further study needs to be done regarding the introduction of foreign styles and the establishment of new styles. Third, further studies must be made with the iconographic and iconological approach. Fourth, more discussions should ensue in the sculpture of pre-historic ages including the rock carved patterns, the sculptural relics retrieved from tombs, and the portrait sculpture of kings and officials. We look forward to having more intensive study and discussions made on those issues. Fifth, posts in universities and museums have recently been filled up mostly by those who specialize in the history of painting, resulting in a fewer number of students wanting to study the history of sculpture. It is, thus, one of the practical tasks to be solved. The history of painting has been the most actively investigated field. One of the problems regarding the history of painting is that the relics are concentrated largely in the Joseon period. Such efforts have already been made but more systematic and activated studies should follow. Second, in-depth and elaborate analysis have been made in the background and the inclinations of the painters by searching the family-tree registers and the private anthologies of the related artists and people, resulting in an encouraging outcome. However, more efforts can be made in combining the socio-philosophical approach, for example, searching for the characteristics of the consumer group and the cost paid for the painting. Third, while active studies have been made in the stylistic development and the school of art, iconological analysis of the landscape or figure paintings has rather been neglected. The crafts comprise various kinds of objects. Among them all, however, the most actively studied field is the ceramics along with the metallic arts. Rarely any study has been made in the rest of the objects. It is absolutely necessary the scope of study be expanded. Also, those who are alrwady involved in this field should expand their boundary of interest. Second, a stylistic approach will have to be boldly initiated in the study of the history of crafts: the studies so far confined in that of the ceramics and metallic arts' history have been made with a formalist approach. Third, an iconological approach also needs to be applied in the study of history of crafts. Architecture is basically an engineering structure, and the history of architecture cannot be understood fully without the knowledge of architectural engineering techniques It is, thus, hard for the art historians to make an easy access to the field. However, the history of architecture also comprises that of the art historical architecture. The task now is to focus on the history of the art historical architecture based on the studies made on the engineering techniques. The history of architecture is recognized as the core part of art history and a comprehensive study of art history in the West. Attention should be paid to the murals, painted patterns and various animal and plant forms sculptured on the structural part of the buildings, so the buildings can be understood as a comprehensive work of art. Second, the history of architecture has been studied with the formalist approach categorizing of architectural parts like pillars, cross beams, and roofs etc. by types. Now, a stylistic approach should be applied in the history of architecture. Third, at present, the study of the history of Korean architecture mostly deals with the wooden buildings. More interests should be shed on stone constructions like the Buddhist cave temples, stone ice storage, and tombs, and at the same time brick constructions like pagodas and buildings. Various kinds of methodology can be applied in the study of the history of Korean art. Here are some suggestions. First, the basis of the study of the art history is to reveal the representational volition of art and establish the art historical view. The representational volition of Korean art can be summarized as the 'activated vitality' during the pre-historic ages, 'incantation' during the Three Kingdoms' Period and Goryeo Period, and 'loyalty and filial piety' and harmony with naturalness' during the Joseon Period. Also, studies should be conducted with various art historic views combined with the cultural historical view at its basis. Second, accurate and strict selection of historic materials should be made. There can be a great number of art objects in various kinds and it's impossible to use all of them. Deciding which of them to deal with as material can differ according to the connoisseurship and the view of the scholar. Thus, the connoisseurship and view is the standard which decides the success or failure of the study of art history. Third, the formalist approach should be applied first, categorizing the selected materials by types and grasping their iconographic features and contents. Also, iconological approach is necessary to find out what the iconographic contents mean, what they symbolize and what significance they carry. Fourth, the stylistic characteristics and beauty of the proportion. shape, volume, and line of each materials should be grasped. and categorized according to the stylistic feature of each epoch, each region, and artists. They can then be arranged in chronological order. Fifth, minute analysis must be made of the changes of style. The method of comparative history and socio-philosophical approach should be applied to draw an accurate interpretation. We discussed first, the representational volition of the Korean art and the art historical view. second, the tasks in the study of Korean art history, and third, methodology of the Korean art history. Art historians should pursue the above mentioned issues with sincerity and re-establish their own view and methodology.