How to stop pawn storms?

I have a question: how do I stop pawn storms, especially near my king? And how do I stop "roller pawns" that advance into uncomfortable territory? For example:

This was something that happened in an OTB game. The position is from memory (I believe the bishop had an escape square so c5 did not trap it, but can't remember where or how) so don't may much attention to it but the h-pawn advancing all the way to h6 caused a lot of trouble and eventually was one of the reasons I lost the game. It was uncomfortably close to my king and I don't really get how I could have stopped it. Another example is this:

I was a pretty low rated player and as you can see missed M1 there and made a few blunders, but the pawn storm-thing was still a thing I struggled with during the game. Now while I can see the pawn storm was a pretty poor idea, I was not and still not able to punish things like that. Does anyone know how to stop kingside pawn storms such as those and punish them in certain cases where it is a disadvantage for your opponent?

To get better at dealing with pawn storms you have to get better at chess in general, the better you get the more you'll know how to deal with stuff like this. Sometimes you can't just fully defend and you might have to rely on counterplay but it's best to calculate lines, make sure to look at every pawn move and evaluate it and see if it'll cause any problems.

The usual reply to a Pawn Storm is a counter-blow in the center... so in the second game your d3-d4 idea was correct. Of course, you should have played Qxh8.

I try to counter attacks on the flank with an attack on the center. Your opponent will be investing material and tempi into their flank attack that their center may be destabilized.

500 elo moment. But yeah makes sense