about this / over this
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about this
Refers to a topic or matter that has just been mentioned; means 'about this topic' or 'on this matter'.
Es gibt verschiedene Meinungen, und hierüber müssen wir noch ausführlich sprechen.
There are different opinions, and we still need to talk about this in detail.
'Hierüber' is a pronominal adverb made up of 'hier' (here) and the preposition 'über' (over/about). It replaces the combination 'über dies' or 'über das' (about this/that) and refers to a thing or topic that has just been mentioned.
Das ist ein wichtiger Punkt. Hierüber sollten wir später noch einmal nachdenken.
That is an important point. We should think about this again later.
Like many adverbs, 'hierüber' (about this) can stand in position 1 in the sentence. In this case, the conjugated verb follows directly after it (inversion).
Hierüber gibt es unterschiedliche Ansichten.
There are different views about this.
'Hierüber' is used mainly in written language and in formal conversations. It often sounds more formal and detached.
Der Ausschuss wird nächste Woche hierüber beraten.
The committee will deliberate on this next week.
The spatial meaning 'über diese Stelle' (over this spot) is very rare today and often sounds old-fashioned. Almost always, the abstract meaning 'über dieses Thema' (about this topic) is meant, referring to a matter mentioned previously.
Der Pfad ist schmal, aber wir müssen hierüber, um zum Gipfel zu gelangen.
The path is narrow, but we have to go over this to reach the summit.
to that / additionally
'dazu' and 'hierüber' can both refer back to a topic that has just been mentioned. 'dazu' is very general and sounds very natural in everyday language: you can say, ask, or think something about that. 'hierüber' more specifically means 'about this topic' and often sounds more formal or written. The words can be confused because 'hierüber' sometimes functions like 'dazu'. If it is simply about an opinion or comment on a topic, 'dazu' usually fits better. If you especially want to emphasize 'about this topic', 'hierüber' fits.
Hierüber möchte die Firma ihre Kunden genauer informieren.
The company would like to inform its customers about this in more detail.
Morgen sprechen wir in der Schule noch einmal dazu.
Tomorrow at school we will talk about that again.