This is an unofficial English translation of the most recent amendment of residency rules, announced on April 22, 2014 in http://gazette.nat.gov.tw/egFront/eng/EngIndex.jsp and http://law.moj.gov.tw/News/news_detail.aspx?id=104491 .
Because legalese is not easy to translate the original Chinese text is provided along and followed by the English translation:
內政部令：修正「外國人停留居留及永久居留辦法」
From the Ministry of the Interior Order: Revision of the regulation covering “foreigners staying, living, and staying as a permanent resident”
公(發)布日期 103-04-22
Issued date: 04-22-2014
內 文
Content
中華民國一百零三年四月二十二日內政部台內移字第 1030951510 號令
修正發布第 8、9、22 條條文；增訂第 22-1 條條文；並自一百零三年
四月二十二日施行
(this is the #1030951510 order from the Taiwanese Ministry of the Interior; revision of the #8, 9, 22; new 22-1; the starting date of mandate from April 22, 2014)
第 8 條 外國人依本法第三十一條第一項規定申請延期居留時，應於居留期限屆滿
前三十日內，檢具下列文件及照片一張，向入出國及移民署提出：
#8 Article, Issue #31, Item #1: Foreigners who wish to apply for extended residency in Taiwan, should send the application package with one photograph, to the “Immigration Office” (出國及移民署) within the last 30 days of the legal staying period:
(Application package)
一、申請書。Application Form
二、護照及外僑居留證。Passport (護照) and ARC( 外僑居留證)
三、其他證明文件。 Other documents
外國人經許可在臺灣地區居留，年齡在二十歲以上，其父或母持有外僑居
留證或外僑永久居留證，且有下列情形之一者，得申請延期居留：
Aliens permitted to reside in Taiwan Foreigners who are 20 years old/or older, and whose father or mother already holds an “Alien Residency Certificate (ARC)” or “Alien Permanent Residency Certificate (APRC)”, and who fulfill the following requirements (qualifications) may apply for the extended residency:
、曾在我國合法累計居留十年，每年居住超過二百七十日。
1. Who has been living in Taiwan legally for at least 10 years, in which he/she has stayed more than 270 days per year.
二、未滿十六歲入國，每年居住超過二百七十日。
2. Who was younger than 16 years old when he/she came to Taiwan and since has been living in Taiwan more than 270 days every year.
三、在我國出生，曾在我國合法累計居留十年，每年居住超過一百八十三
日。
3. Who was born in Taiwan, and has been living in Taiwan for 10 years, and lived for more than 183 days in Taiwan in each of these years.
前項外國人應於居留期限屆滿前三十日內，檢具下列文件及照片一張，向
入出國及移民署提出：
Foreigners who are qualified (as listed above) should send in the application package and one photograph to the “Immigration Office” (出國及移民署) within the last 30 days of the legal staying period:
一、申請書。 1. Application Form
二、護照及外僑居留證。2. Passport and Alien Resident Certificate
三、親屬關係證明。3. Documents proving the relationship to parents
四、其他證明文件。4. Other supporting documents
第 9 條 下列外國人之外僑居留證，其效期最長不得逾一年：
#9 Article. The Alien Residency Certificate (ARC, the residency permit) issued to the following aliens can only allow for one year residency:
、在教育主管機關立案之學校或大學附設之華語文中心就學之人員。
1. Foreign students who study in Chinese language centers of any universities/colleges recognized by the Ministry of Education.
二、經教育或其他有關主管機關核准，在我國研習、受訓之人員。
2. Foreigners studying or undergoing training with the approval of the Ministry of Education or any other Government Ministries.
三、外籍傳教及弘法人士。
3. Foreign missionaries and monks.
四、與臺灣地區設有戶籍國民結婚，初次申請依親居留者。
4. A foreigner married to a Taiwanese citizen (the Taiwanese citizen must have the residency record in Taiwan), if this is the first time that this foreigner applies for the relative (spousal)-dependent residency.
五、其他有居留需要之人員。
5. Foreigners with other needs for long-term residency.
前項第一款人員，係經教育部專案核列大學之獎學金受獎者，得不受最長
有效居留期間一年之限制。
As for #1 (foreign students), if the foreign student has been awarded a scholarship provided from the Ministry of Education to the University in specific cases will not be limited for one-year residency only. (This means students with scholarships from the Ministry of Education can stay longer than one-year)
前條第二項外國人申請延期居留經許可核發之外僑居留證，其效期自原居
留期限屆滿之翌日起延期三年，必要時，得再申請延期一次，期間不得逾
三年。
(“前條第二項”—the wording here is not clear as meaning for the #2 qualification under #8 Order, or under #9 Order) Foreigners who meet the qualifications of “前條第二項” may apply for extension of the Alien Residency Certificate. The extension is allowed for 3 years starting from the very last day of previous residency. When necessary, a second extension is allowed for 3 more years (but cannot exceed 3 years).
第 22 條 外國人來臺投資，或依就業服務法第四十六條第一項第一款至第七款及第
四十八條第一項第一款應聘來臺，或經外交部專案核准居留，於居留效期
屆滿前，有必要者，本人及其原經核准居留之配偶、未成年子女，得以書
面敘明理由，向入出國及移民署申請延期，經核可後，得於原居留效期屆
滿後六個月內離境。
#22 Order. The Foreigner who came to Taiwan for business investment, or is hired to work in Taiwan according to the Professions/Occupation/Service Law #46, Issue #1 (#1-#7), and Law #48, Issue 1 (#1) [或依就業服務法第四十六條第一項第一款至第七款及第四十八條第一項第一款], or is permitted to stay long-term in Taiwan by the Ministry of Foreign Affairs (with special cases), if needed, before the last date of legal residency, this Foreigner with his/her spouse (who also has legal residency originally) and their children who are not adults, may apply extended residency to the “Immigration Office” (出國及移民署) with a written application (the application will have to explain the reason of staying as”得以書面敘明理由”). If it is approved, the Foreigner may stay for extra 6 months.
第 22-1 條 外國人來臺就學，於居留效期屆滿前，有必要者，得以書面敘明理由，向
入出國及移民署申請延期。
依前項規定申請居留延期經許可者，其外僑居留證之有效期間，自原居留
效期屆滿之翌日起延期六個月。
#22-1 Order. Foreigners who come to Taiwan for studying (as foreign students), before the legal residency date, if necessary, the foreign student may use a written application to explain the reasons of extension of residency and apply to the “Immigration Office” for extension of residency. If it is permitted, the Foreigner may stay for extra 6 months.
Here is the same text but with most of the Chinese removed for easier reading:
From the Ministry of the Interior Order: Revision of the regulation covering “foreigners staying, living, and staying as a permanent resident”
Issued date: 04-22-2014
Content
(this is the #1030951510 order from the Taiwanese Ministry of the Interior; revision of the #8, 9, 22; new 22-1; the starting date of mandate from April 22, 2014)
#8 Order, Issue #31, Item #1: Foreigners who wish to apply for extended residency in Taiwan, should send the application package with one photograph, to the “Immigration Office” (出國及移民署) within the last 30 days of the legal staying period:
(Application package)
1, Application Form
2, Passport (護照) and Alien Resident Certificate (ARC, 外僑居留證)
3, Other supporting documents
Aliens permitted to reside in Taiwan Foreigners who are 20 years old/or older, and whose father or mother already holds an “Alien Residency Certificate (ARC)” or “Alien Permanent Residency Certificate (APRC)”, and who fulfill the following requirements (qualifications) may apply for the extended residency:
1. Who has been living in Taiwan legally for at least 10 years, in which he/she has stayed more than 270 days per year.
2. Who was younger than 16 years old when he/she came to Taiwan and since has been living in Taiwan more than 270 days every year.
3. Who was born in Taiwan, and has been living in Taiwan for 10 years, and lived for more than 183 days in Taiwan in each of these years.
Foreigners who are qualified (as listed above) should send in the application package and one photograph to the “Immigration Office” (出國及移民署) within the last 30 days of the legal staying period:
1. Application Form
2. Passport and the “Alien Resident Certificate”
3. Documents proving the relationship to the parents
4. Other supporting documents
#9 Order. The Alien Residency Certificate (ARC) for the following foreigners can only allow for one year residency:
1. Foreign students who study in the Chinese language centers of any universities/colleges that are recognized by the Ministry of Education.
2. Foreigners studying or undergoing training with the approval of the Ministry of Education or any other Government Ministries.
3. Foreign missionaries and monks.
4. A foreigner married to a Taiwanese citizen (the Taiwanese citizen must have the residency record in Taiwan), if this is the first time that this foreigner applies for the relative (spousal)-dependent residency.
5. Foreigners with other needs for long-term residency.
As for the #1 (foreign students), if the foreign student is awarded with a scholarship provided from the Ministry of Education to the University in specific cases will not be limited for one-year residency only. (that means students with scholarships from the Ministry of Education can stay longer than one-year)
(“前條第二項”—the wording here is not clear as meaning for the #2 qualification under #8 Order, or under #9 Order) Foreigners who meet the qualification of “前條第二項” may apply for extension of the Foreigner Residency Card. The extension is allowed for 3 years starting from the very last day of previous residency. When necessary, the second extension is allowed for 3 more years (but cannot be longer than 3 years).
#22 Order. The Foreigner who came to Taiwan for business investment, or is hired to work in Taiwan according to the Professions/Occupation/Service Law #46, Issue #1 (#1-#7), and Law #48, Issue 1 (#1) [或依就業服務法第四十六條第一項第一款至第七款及第四十八條第一項第一款], or is permitted to stay long-term in Taiwan by the Ministry of Foreign Affairs (with special cases), if needed, before the last date of legal residency, this Foreigner with his/her spouse (who also has legal residency originally) and their children who are not adults, may apply extended residency to the “Immigration Office” (出國及移民署) with a written application (the application will have to explain the reason of staying as”得以書面敘明理由”). If it is permitted, the Foreigner may stay for extra 6 months.
#22-1 Order. Foreigners who come to Taiwan for studying (as foreign students), before the legal residency date, if necessary, the foreign student may use a written application to explain the reasons of extension of residency and apply to the “Immigration Office” for extension of residency. If it is permitted, the Foreigner may stay for extra 6 months.