Ace's tattoo.

Ace is Luffy's brother in law which meet luffy the first time at a young age. He made his tattoo on his right arm and named it ASCE with the S crossed out with an X. Without the S crossed with an x the tattoo, is his name ACE. 

The S crossed as a tattoo means allot to Ace because, when he was young his best friend was Sabo. After some time Sabo went out to sail in the ocean with a small ship. when he exactly set sail people bombarded the ship which he was in and then died on the spot. The S with an X on it is because, his name was Sabo so he decided to make his first letter of his name with a cross bone as his pirate flag. Ace made a tattoo of his flag to keep him in his memories.

The other tattoo which Ace have on his back is his pirate crew flag symbol. He's not the captain of the crew but he's a crew member, subordinate and the tattoo and flag is of the white beard name which he's in.

Ace's ASCE tattoo is first shown at 0:01 minutes and the white beard tattoo in the video first is shown at 0:03 minutes.
       

Luffy's tattoo.  

Luffy's tattoo is 3D2Y which he made it for a reason. The 3D crossed out with an X means not 3 days and 2 d means 2 days. He did the tattoo to communicate with his crew members because luffy "the captain" had made some change of plans for the safety of his crew. 

The reason that Luffy made a tattoo on his right arm and 3D2Y because his crew members where all in different places in the world, not only in yhe first half of the red line. Before they all came apart, they had agreed that they will meet again in 3 days at  Sabaody in a specific bar. The captain "luffy" made some change of plans because if they meet in three days the marines and the admirals will attack them, so Luffy decided that all of them will meet in 2 years and not in 3 days. So he made a tattoo that the marines will not notice and only his crew will understand it.