Binary stars interact in a variety of ways depending on...
Winds
Colliding winds in early-type stars, wind accretion in high-mass XRBs,...

Luminosity
Surface heating by a companion X-ray source, photoionization of the wind in symbiotic stars, ...

Magnetic Fields
The strong stellar magnetic field in AM Her stars...

Binary Separation
Tidal effects in close binaries: large tides, distorted winds, synchronization, mass transfer,...