I've been reading this manga from it's beginning. I think we can all agree that we haven't seen enough of Shanks powers. But, let's see some examples of him demonstrating his powers:
When we first saw him with Luffy (in the first episode) and we see little of his fighting skills, mostly just his spirit, which he demonstrates against Higuma and then to the Sea King where, he demonstrates his Haki.
Then after 10 years, with only one arm left, he is been visited by Mihawk on an island. We all know Mihawk is the best swordsman in the OP world. A guy won't just cozy up to any ordinary pirate after all for a drink, in celebration of Luffy's first bounty.
After which we learn that they've had regular matches with one another, which means in terms of powers he has to be very strong to be a match for Mihawk. Also then he demonstrates that he can take a blow from the Yonko. And when he entered the Whitebeard's ship his haki not only knocked out a lot of Whitebeard's crew, but also damaged the ship. Also this caused Whitebeard's scar to ache and have Marco and Jozu commend about his spirit.
Also before the Summmit War Arc he was fighting another Yonko, Kaido, which According to Law, he is "the strongest creature in the world" and an ally of Donquixote Doflamingo.
After that events, we saw him in Summit War Arc where he stopped Akainu with Armament haki. And then he asked Blackbeard which until then he didn't fear anyone to fight (Whitebeard, was an exception) and he said that it's not time yet for them to fight. He understood on that moment he isn't ready to fight Shanks, which it means a lot, since he stopped the war, even Sengoku respects.
While Shanks hasn't been in a lot of fights and Oda haven't show us yet Shank's skills, from the above mentioned facts, I think we can all agree that he deserves to be amongst the Yonko.
Also It's not just him that's strong, his crew members are too, Ben Beckman was able to make Kizaru stop for a moment during the Summit War Arc.