Is there such a beast?
Playing from most recent to oldest makes no sense to me, but I don’t see a way to change it.
Overcast allows you to sort oldest to newest or vice versa.
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What is your current player, John?
like already mentioned, Overcast support sorting from oldest. Pocket Casts also support that. While Apple Podcast and Castro don’t.
If you want continuous play, Overcast might be your best bet. Otherwise, you may chose between Overcast and Pocket Casts.
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I once reviewed Overcast, Pocket Casts, Apple Podcast and Castro, then lists the feature and pros-cons on OmniOutliner. The conclusion, I decided to use continue using Pocket Casts.
I didn’t mention “sorting”, but I will just leave the exported outlines to plain text here, maybe it helps someone. Note that this document is 4 months old, so maybe there are new features / improvements not mentioned here.
- Pocket Casts
- + chapter marker
- ++ episode progress also shown on chapter marker
- ++ chapter image works
- +++ chapter image zoomable
- + timestamp in show notes works
- + good playlist management
- + iPad app
- + web player
- $ desktop app
- - desktop app is electron
- $ trim silence
- - trim silence is not very good
- $ voice boost
- + reasonably priced premium plan
USD1/month
- + listening history
accessible from profile→history
- ++ can play video podcasts
- - search limited to podcast feed
- Overcast
Reviewed on free mode. Premium has no free trial.
- + chapter marker
- ++ episode progress also shown on chapter marker
- ++ chapter image works
- + simple, lightweight feel interface
- + search can discover any show notes and title in any podcast feed
- + timestamp in show notes works
- + smart speed
automatically increase or decrease the podcast play speed
- + voice boost
- + iPad app
- + web player
- - web player is limiting and confusing
- - no desktop app
- - no listening history
- - cannot play video podcasts
- - show notes often not formatted correctly
- Apple Podcast
- + desktop app
- + iPad app
- + web player
- - web player is hard to access, and often prompt to open app
- + listening history
accessible via home
- + can play video podcasts
- + search can discover any show notes and title in any podcast feed
- -- show notes does not formatted correctly
- Castro
- + trim episode sneak peek and share
- + chapter marker
- ++ episode progress also shown on chapter marker
- ++ chapter image works
- + listening history
easily accessible from feed lists
- $ voice boost
- $ trim silence
- + this feature is very good
- + the trimmed progress is shown individually per podcast
- ++ incremented live
- - cannot play video podcasts
- - no iPad app
- - no desktop app
- - no web player
- - search limited to podcast feed
note: the ability to play video is essential for me to listen to TWiT 
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Pocket Casts definitely does this. One of my playlists on that app (Pocket Casts calls them “filters”) is just every unplayed episode of every podcast I subscribe to, sorted oldest to newest.
That filter currently has (checks iPhone) 434 episodes. I don’t think I’m going to get caught up by the weekend.
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Thanks for the info and detail @ybbond , @geoffaire , and @MitchWagner !
Currently using Apple’s app, previously Airr, before that Overcast.
Edit: Pocket Casts seems intuitive, and can sort ‘correctly’. I’ll give it a try.
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Downcast has this and other sorting options.
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Apple podcasts has this, go to the specific show and go to settings and it’s an option for oldest to newest. I’m on 14.5 rc, so this could have just been changed with the announcement of subscriptions and such.
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Well they could have hidden that a little better 
Thanks! Now I don’t lose history on all my shows.
Worth noting Overcast lets you sort both Unplayed and All lists oldest > newest and newest > oldest. You can set both list sort orders in each Podcast’s settings.
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