Fallout 4 allows you to have deep relationships with companions, both based on your will to get into bed with them or just have a friendship. The latter can also reveal very satisfying, although we think you won't be much interested in it, at least if you played The Witcher 3: Wild Hunt or Mass Effect and know what to expect from this kind of "deep relationships".
By the way, the first thing you need to do is reaching the maximum level of affinity with them. Each time you get a new level, go talk with your companions to see if you have unlocked the "romantic" or "flirtatious" dialogue options; if you have done that, check if you have enough Charisma and Luck to deal with them by doing some trial and error – be sure you quick save before starting with it.
There's a lot more to get, anyway, in case you manage to reach the maximum affinity with your companions. Here's a list of the rewards you can gain by simply becoming a true friend to them.
Don't forget to let us know who is your favorite companion in the comments below. Check out full Fallout 4 Wiki Page