We are a team of 12 developers in our local office plus five to six remote guys. How do you integrate remote developers? On a technical level (video conferencing, IM), but also on a social/personal level (team spirit etc.).
Depends how far the remote team is and the budget available for the team building activities. Craig Rich already mentioned some of the great activities you can do to integrate all team members.
In my prior business we did regular visits (both directions), job swaps for extended periods, provided collateral / brand items from our business so that their office "felt" like ours, and included them in all general communications about the products that they were involved in building. We were using agile techniques so they were intrinsic to the overall communication anyway.
Are their time zone drastically different? Socially you should integrate something like slack and conferencing should be mandatory and should occur as often as you need it.
Live video conference including CTO, CEO and decision makers.
I also faced many interviews reliability can be judged by the attitude during the call.