orthography - What are the most obscure kanji?

To my understanding, there are standardised kanji that have either:

• No reliable information on how they are to be pronounced OR


• No reliable information on what they mean OR


• All of the above.

Do these kanji exist, and if so: What are the current hypotheses on what they mean/how they are pronounced?

Answer

We call them:

• No reliable information on how they are to be pronounced → 音【おん】（未詳【みしょう】／不明【ふめい】）字【じ】


• No reliable information on what they mean → 義【ぎ】（未詳／不明）字


• All of the above → 音義（未詳／不明）字

幽霊文字 in @naruto's answer is usually considered as a subset of them (technically, meaning/pronunciation of some 幽霊文字 are easily inferrable so they're not true subset).

Some Chinese Characters have unknown meaning/pronunciation even they have reliable source, because it's clearly written in dictionaries that "音未詳"/"義未詳"/"音義未詳". When those massive dictionaries were compiled, they tried to collect characters from all available documents. Some characters only have too sporadic (or single) specimens to reasonably guess what they are. Some others are from previous dictionary with whose description about meaning/pronunciation are lost or unrecorded. The Unicode standard contains a numerous number of those characters because it has unconditionally incorporated all entries in the authoritative dictionaries.

While they have possibility to be identified through investigation, there was no research encompassing the entire encoded characters as far as I know, thus many of them are just left to be determined.