user75805: I understand that P2SH addresses are used to allow "segwit unaware" wallets to create outputs spendable by segwit wallets (please correct me if I got something wrong). For new clients I think I got it: they will check that the script cointaned in the witness matches the script hash and execute it.
What I do not understand is how this  output is spendable by a segwit aware client to the eyes of an old client. Because it clearly doesn't look like an anyone can spend. How does it work?
Thanks.

user38482: There was a longer discussion thread in bitcointalk, I proide two references:
https://bitcointalk.org/index.php?topic=2333913.msg23758008#msg23758008
https://bitcointalk.org/index.php?topic=1682183.msg21389041#msg21389041
(Both threads are worthwhile to read in it's entirety). 
In short: before nodes talk to each other, they verify the capabilities. And a segwit node would reduce the information for a non-segwit node, so that he can understand the transaction details.  

75805: <p>I understand that P2SH addresses are used to allow "segwit unaware" wallets to create outputs spendable by segwit wallets (please correct me if I got something wrong). For new clients I think I got it: they will check that the script cointaned in the witness matches the script hash and execute it.</p>

<p>What I do not understand is how this  output is spendable by a segwit aware client to the eyes of an old client. Because it clearly doesn't look like an anyone can spend. How does it work?</p>

<p>Thanks.</p>
 38482: <p>There was a longer discussion thread in bitcointalk, I proide two references:</p>

<p><a href="https://bitcointalk.org/index.php?topic=2333913.msg23758008#msg23758008" rel="nofollow noreferrer">https://bitcointalk.org/index.php?topic=2333913.msg23758008#msg23758008</a></p>

<p><a href="https://bitcointalk.org/index.php?topic=1682183.msg21389041#msg21389041" rel="nofollow noreferrer">https://bitcointalk.org/index.php?topic=1682183.msg21389041#msg21389041</a></p>

<p>(Both threads are worthwhile to read in it's entirety). 
In short: before nodes talk to each other, they verify the capabilities. And a segwit node would reduce the information for a non-segwit node, so that he can understand the transaction details.  </p>
