What did the Apostolic Fathers believe regarding the state of the dead and the afterlife?

In the context of related debates such as: - [Bipartite](https://en.wikipedia.org/wiki/Bipartite_(theology)) vs. [Tripartite](https://en.wikipedia.org/wiki/Tripartite_(theology)) natures of man, - [Soul sleep](https://en.wikipedia.org/wiki/Christian_mortalism) vs. Consciousness during the [intermediate state](https://en.wikipedia.org/wiki/Intermediate_state) , and - [Annihilationism](https://en.wikipedia.org/wiki/Annihilationism) / [Conditional immortality](https://en.wikipedia.org/wiki/Christian_conditionalism) vs. [Immortality of the Soul](https://en.wikipedia.org/wiki/Immortality#Religious_views) , I think it would be quite helpful to know the views held by the Apostolic Fathers, as they had the unique privilege of receiving direct or almost direct teaching from the Apostles themselves. I checked the site assuming someone had probably already asked a similar question in the past, but I'm a bit surprised to say that it appears no one has (please let me know if I overlooked something), so here we go: **Question**: What is an overview of beliefs held by the Apostolic Fathers regarding the state of the dead and the afterlife? What happens when (and after) we die according to the Apostolic Fathers? **Note**: by [Apostolic Fathers](https://en.wikipedia.org/wiki/Apostolic_Fathers) I mean: > [...] core Christian theologians among the Church Fathers who lived in the 1st and 2nd centuries AD, who are believed to have personally known some of the Twelve Apostles, or to have been significantly influenced by them. ____ See the answers to this [question](https://hermeneutics.stackexchange.com/q/73790/38524) for an example of an intense exegetical debate on these controversial subject matters. See also this recently asked [question](https://hermeneutics.stackexchange.com/q/73816/38524) for another ongoing debate. _____ Related: https://christianity.stackexchange.com/q/81207/50422