Chinese celadons (greenware) are among my favourite pieces. They are usually plain yet exquisite and so pleasing to behold. Some have incised peony, chrysanthemum flowers, lotus patterns or applique of fish or phoenix. The zenith of quality celadon production was during the Song Dynasty (10-12c) and the most famous kiln site was in Longquan.
After applying a green glaze, the piece is high fired in the kiln through an oxygen reduction process. If oxygen gets in, it will turn out into golden or brown instead of the beautiful sought after green. Moreover, if the firing is not regulated precisely (think its 1200 degree celsius) the outcome is stoneware rather than porcelain celadons.
The highest quality ceramics made for the emperor or officials are today known as imperial or official ware. Collectors pay a fortune for them. The only one I have is seen in the first photo, a bluish green (called mystic green) dish. I bought it in Jakarta over a quarter century ago. The earlier provenance is unknown but was probably a royal gift to a local dignitary. There were increasing trade during this period with SE Asia and among the items were chinese exportware ceramics, including celadons.
"Chinese Celadons and other related wares in Southeast Asia" compiled by the Southeast Asian Ceramic Society and published by Arts Orientalis Singapore provides photos and information on the subject.