Are there real-life alternatives to the chain+derailleur combo?
Belt drive + Internally Geared Hub is a popular combination.

Existing systems are based around a gates carbon belt drive. See the Breezer Beltway series bikes. Also Reeb Cycles began offering belt drives for mountain bikes when they first came to market.

Also, now there is a breakable belt system called Veer that doesn't require a frame cutout (though uses cogs somewhat different from older belt drive systems) which could be used in configuration with an internally geared hub (when their new pro-version comes out). Currently it appears to be singlespeed only. 

Though this is still rather similar to a chain drive system, there is less regular maintenance needed to keep the drivetrain clean as wear is not as damaging on the belt drive system. Performance is different with an IGH hub though. 

There are also shaft driven bikes which engage with a standard internally geared hub (instead of a cassette like mechanism). See related SE question with some detail. Any experience with shaft driven bikes?