What causes blue smoke from your car?

This depends:

• Diesel engine cold start, engine wear, damaged or worn injection system

Gasoline engines display blue smoke from oil usage:

• If a puff of blue smoke on cold start, valve guides are leaking slightly
• A puff of blue smoke after a deceleration with no throttle applied, valve guides are worse than he above example and oil usage may be starting to be an issue due to this.
• Blue smoke at idle and most times when the engine is at low throttle or medium throttle settings. This engine is badly worn or has been badly overheated damaging the piston ring seal
• Cloud of blue smoke at high RPM high throttle settings. This engine has "Ring Flutter" and will require new pistons and rings to correct.