An old textbook I still have refers to Japanese years using era names (元号), such as 平成六年 for the 6th year of the Heisei Era, or 1994. In the wild, though, we see a lot of plain 4-digit decimal years; some institutions, like NHK news, provide both, such as: "2015年 (平成27年)". I asked a native speaker at our conversation group: how commonly used are 元号 years outside of textbooks?
His answer: most people, in casual situations, use decimal years; but official documents, both corporate and governmental, tend to use 元号. Doing so honors a tradition dating back more than 1,300 years, and brings up some interesting points regarding the Japanese Emperor.
In Japan the current Emperor's given name (in 2015, Akihito) is not used. To refer to him, instead the term 天皇陛下 (his Majesty the Emperor) is used; or more formally, 今上天皇 (the current Emperor). He acceded to the throne in 1989 and began the Heisei Era (平成時代), starting with 平成1年 (there is no year zero). The term 元年 (origin year) is also used for year 1 of an era.
By custom, at Akihito's death, he would be given the posthumous name 平成天皇 (Emperor Heisei) and the 平成時代 will come to an end. In other words, the name of his reigning era is set aside for him. This last happened in 1989 when Akihito's father, Hirohito, was named Showa (昭和) as his eponymous era (1926-1989) was brought to a close.
Only at the start of Akihito's reign was the 平成 name unveiled. By custom 元号 names are a pair of kanji with positive connotations of tradition, peace, brightness, and so on. 昭和 is literally "shining" + "harmony/Japan". 平成 is "peace" + "become". The names must also be easy to read and write, and not duplicate another era or an existing Japanese word.
The current Emperor is the 125th to take the throne, and continues a string of 元号 eras dating back to 701 CE (大宝 era). The tradition of One Era, One Emperor, however, is much newer, starting in the Meiji (明治) Era in 1868. Before that, more than one era was associated with a single Emperor (and sometimes vice versa). As a curiosity, beginning and ending years may be less than 365 days long, as an era starts on the date the Emperor takes the throne, while year numbers increment on January 1.
The next transition, scheduled for spring 2019, will put "One Era, One Emperor" to the test—with some implications that did not exist one or two eras earlier.
In 2016, Akihito announced a plan to abdicate the throne on January 1, 2018 in favor of his crown prince son Naruhito. (Later, in December 2017, the date was moved to April 30, 2019.) This last happened 200 years ago and brings up a number of questions, including handling of the era changeover.
Businesses and makers of calendars are asking for advance notice of the new era name, which is traditionally not done. Also, the Unicode Consortium will also need to create a new character for the name. Why is this the case, if all era names are constructed from existing kanji? Because Japanese computers use a compressed single character for recent names, and Unicode fulfills that need (as far back as the Taishou era). Unicode 12 is scheduled for early March 2019, but the new era name may not be revealed until afterward, making a 12.1 release necessary.
Furthermore, some computers from earlier than 1989 are still in use, and could not be patched for the Heisei changeover; in that case, the users tolerate "overflowed" years such as "昭和 93" for 2018. In 7 years, however, "昭和 100" may cause further Y2K-type problems.
As of 2018, Akihito is still 今上天皇: the current emperor. After he abdicates, how will people refer to him? The 平成天皇 name is traditionally posthumous, but may still be applied as 平成 comes to an end.
お疲れ様, thanks for reading!