In Dragon Age: Inquisition, there are companions and advisors who help you throughout the game. There are three advisors available, and each one has information about different aspects of the Inquisition and aspects of the game. Because you are the head of the Inquisition, you'll need to take their wisdom into account when you are deciding on different courses of action. You can also have a romantic relationship with certain advisors if you choose.
Cullen is a former Knight-Captain of the Templar Order, and he is in charge of the military forces. Cullen was also in the previous two Dragon Age entries. The Inner Circle quests available from Cullen are Perseverance, Happier Times, and Before the Dawn. If you are interested in starting a romance with Cullen, you'll need to be playing a female human or elf. If you are in another relationship with someone, don't bother trying – Cullen is only interested if you are completely single. You can start romancing this character after arriving at Skyhold. The most important thing to remember is not to ever discuss Lyrium with Cullen. If you do, your romance will end before it even begins.
Josephine was once an Antivan family ambassador. Now, she serves as the ambassador and chief diplomat for the inquisition. She offers the Inner Circle quests Of Somewhat Fallen Fortune, Heraldry From a Herald, and An Unexpected Engagement. Josephine can be romanced by any character, no matter of race or gender. After you arrive at Skyhold, you can start to form a relationship with her. Josephine's first appearance in is this new Dragon Age entry.
Leliana was an agent of the Chantry, and a former companion of other Dragon Age heroes. She has in both previous entries. Now, she is the Spymaster of the Inquisition. She offers the Inner Circle quests The Left Hand of the Divine and Under Her Skin. You cannot romance Leliana, no matter what character you are playing.
