In a rest of the world scenario, transits on a single ticket (say EK LHR-DXB-NRT), you would get both boarding passes when checking in, bags would be tagged to NRT and then you would only see it in Tokyo. The transit in Dubai would not have customs or immigration and there would only be security.
Only in case of leaving the airport as part of a layover, you would clear immigration & customs in DXB to be able to leave the airport but bags would still be checked-in.
Routine transits will almost always be like this.
If you flew DL LHR-ATL-NRT, you would clear immigration, customs, collect your bags and then drop them at a bag drop-off which is usually close to customs. There will also be security once you reach the departures concourse. The same applies for an international to domestic connection.
For that reason, it is advisable to have sufficient time to make your connection though Delta will put you on the next flight if you miss. I suggest checking the Department of Transport's website for average processing times for the time at which your flight arrives. In places like JFK, 120 minutes and above can easily be spent at immigration. Not too sure about ATL.
Ro