They left behind a family: a husband/wife and a son, to whom they want to return.

In our time they partnered with a police agent.

(Who happens to be of the opposite sex.)

(And with which they have a non-romantic relationship.)

They also have a voice in their ear to help them out in their quest: Katrina and her witch powers for Ichabod and Alec and his technology for Kiera.  Because witchcraft and technology are two sides of the same coin.

Both Ichabod and Kiera had to get used to our technology and way of life, but they also brought some of their own.  They also kept their era clothes, both of which look uncomfortable and have a high collar.

If they ever meet, they are the only people on the planet who can really understand each other.