Royal Caribbean's second quarter earnings beat expectations.

The cruise company wants the public’s help through social media.

The industry was hurt by the recession and a series of disasters at sea.

Carnival relieves its longtime CEO of his CEO-ship. Overall the company, which includes several lines, is making a profit. Carnival Cruise, which has had all the mishaps, is suffering.

Carnival's sullied cruise ship Triumph relaunches today. Can the ship bounce back after its public relations disaster earlier this year?

Probably not, say lawyers, unless you've suffered physical injury. As a gesture of goodwill, Carnival is offerering a full refund, a voucher for a future trip, and $500.

The cruise business is emerging from the down economy thanks to lower fuel prices, bigger boats and more fees for perks like alcohol and excursions.