Recently, in a languagehat thread about the era name Genroku and the dyad seppuku/harakiri, I mentioned as a source a 2003 book edited by YONEDA Yusuke and named Rekidai tennō/nengō jiten 歴代天皇年・号事典, literally "Encyclopedia of successive emperors and era names" (2003, ed. YONEDA Yūsuke 米田雄介). Note the word rekidai 歴代, "successive [generation-wise]": why such a specific title?

Because there are dozens of figures in Japanese history who, though referred to with the title tennō (emperor) or an equivalent in at least some sources, were not included in the succession chart for one reason or another when it was finalized in the early 20th century. Thus, they are not rekidai tennō, and not included in Yoneda's book.

Wikipedia has a nice list of such persons, divided into categories that include:

• Tsuison tennō 追尊天皇, granted the title posthumously. Example: Emperor Kyōkō, who was only recognized as such by the Meiji court in 1884 despite his son Emperor Kōkaku having agitated so vigorously for this in the 1790s that the shogunate put him under temporary house arrest — this "Title Incident" (尊号事件) is now considered significant as an example of the re-emerging disagreements regarding imperial authority that would eventually culminate in the Meiji Restoration.
• Sonshō tennō 尊称天皇, granted the title while living despite not actually being emperor. Example: Go-Takakura-In, who upon the accession of his ten-year-old son Emperor Go-Hirokawa in 1221 was declared 太上天皇 da(i)jōtennō, "grand upper [previous] emperor", a title usually reserved for emperors who had abdicated, so that he could run things from behind the scenes as was customary at the time.
• Self-declared emperors whose reigns either never got off the ground or did not end well. Examples: Self-declared "New Emperor" (新皇) TAIRA no Masakado (beheaded by cousin, nasty business); "Emperor Kumazawa", a Nagoya man named KUMAZAWA Hiromichi who rose to fame during the post-WWII occupation claiming that his (alleged) descent from the 14th-century Southern Court made him the true emperor of Japan, which in turn meant that the responsibility for the war lay on the shoulders of a pretender instead. Ironically, Kumazawa was himself besieged by a wave of "Kumazawa Pretenders" who agreed with all his claims except for the one about him being next in the line of imperial succession. (No doubt this didn't sound quite as zany in the 1940s, when the validity and structure of the imperial system was under serious attack from many sides — note that the GHQ report linked above reports that left-wing newspapers supported Kumazawa as an attack on the actual emperor and his authority.)