Last Exile is an anime about a war going on between Anatory and Disith, two lands separated by the Grand Stream, a large area in the sky filled with harsh winds and many other obstacles.  Many years ago, Anatory sent two men through the Grand Stream with a message of peace to Disith, but they never made it.  Peace was never achieved and the war raged on for many more years.  The Guild ruled the world and kept the war going between the two nations because they controlled Exile (apparently, whoever controls Exile makes the world how they want it to be).  The leader of the Guild, Maestro Delphine, saw to it that the land dwellers only got as much as they needed while she indulged in the finer things.  She made sure that the war continued and was probably the one responsible for the two men never reaching Disith.

Claus Valca was a young man living in the village of Norkia with his best friend, Lavie Head.  Their fathers were the two men sent through the Grand Stream to Disith, so they had to survive on their own for quite some time.  They did this by learning how to fly their fathers' vanship and becoming couriers.  They loved flying and were content until they came upon a young girl named Alvis Hamilton and were told to bring her to the Silvana, an airship famous for being nearly invincible.  They had second thoughts, but Claus wanted to protect Alvis at all costs.  They got her to the crew of the Silvana, but Claus and Lavie brought themselves further into the war then they ever wanted to when they decided to go on the Silvana themselves.  This is where Claus met Tatiana, and when Claus and Lavie's lives were forever changed.

Tatiana Wisla was the leader of the Silvana's vanship fleet.  She was first in her class at the military academy and was a bit too full of herself.  She did have feelings, but she hid them behind the person she thought she was supposed to be.  She had been through a lot in her life (she was from a noble family, but they were "Abandoned Nobles") and felt like she needed to prove herself at every obstacle.  All of the mechanics were scared of her because of her ways, but she was still the best pilot in the fleet.  She helped Claus when he first came to the Silvana, but he didn't really register to her at that point.

While on the Silvana, Claus wanted to try flying a fighter vanship with Lavie, but Tatiana didn't think it was a wise idea.  He was allowed to fly one against her wishes, but Lavie wasn't ready (she blacked out during the battle).  After that, Claus flew with different people each time he was needed, and at one point, Tatiana requested that he be her navigator.  This was not because she liked him, but because he had put a strain on her relationship with Alister, her usual navigator.  This battle did not end well, though, and the two ended up crashing in the desert.  Tatiana became very unstable thinking about the battle, but Claus helped her to come back.  They really got to know each other during this time and came to care about one another.

Once they made it back to the Silvana, Tatiana tried to make Claus leave so he wouldn't get hurt, but he wanted to remain a fighter pilot.  Seeing them together made Lavie very jealous, but Claus didn't realize her feelings.  He had changed and grown up during his time with Tatiana, as had she.  She got him thinking about his reasons for flying and wanting to be in the skies, and he had her thinking about who she really was, who she wanted to be.  After Claus had been taken by the Guild with Alvis and separated from everyone for quite a while, he realized the answer to Tatiana's question.  As he made his way to the Grand Stream, Tatiana was his navigator at one point, and she finally accepted his answer to her question: he wanted to protect Alvis and his friends at all costs.

The ending of Last Exile was one of the best as far as anime shows go.  Claus and Tatiana's relationship may not have been as forward as Dunya and Mullin's, but there was nothing saying that they weren't together.  The war was over and everyone was happy.  I believe that Claus still flew with Lavie (she was his navigator for pretty much his whole life after all), but his heart was with Tatiana.  I don't know how many years passed between the war ending and the end of the show (it had to be at least four because one couple was able to get married and have two kids already), but Claus and Tatiana both had time to grow up a bit more.  I think that they probably continued their relationship during this time and would probably get married at some point in the future.

This quote is from when Claus and Tatiana were flying in her vanship near the end of the show.  He was telling her about how he felt like a bystander and how he didn't feel like he could save anyone.  Two guild ships then attacked them and Claus came up with a plan to get rid of them.  Then, Tatiana said this to lift his spirits.

Tatiana:  "Claus, you are far from being just a bystander.  You’ve kept Alvis safe, haven’t you?"