Switch to Eyedropper tool and sample fill and/or stroke

Alt-click + Live Paint Bucket tool

Option-click + Live Paint Bucket tool

Switch to Eyedropper tool and sample color from an image or intermediate color from a gradient

Alt + Shift-click + Live Paint Bucket tool

Option + Shift-click + Live Paint Bucket tool

Select opposite Live Paint Bucket tool options (if Paint Fills and Paint Strokes are currently selected, switch to Paint Fills only)

Shift + Live Paint Bucket tool

Shift + Live Paint Bucket tool

Fill across unstroked edges into adjacent faces

Double-click + Live Paint Bucket tool

Double-click + Live Paint Bucket tool

Fill all faces that have same fill and stroke all edges that have same stroke

Triple-click + Live Paint Bucket tool

Triple-click + Live Paint Bucket tool

Switch to Eyedropper tool and sample fill and/or stroke

Alt-click + Live Paint Selection tool

Option-click + Live Paint Selection tool

Switch to Eyedropper tool and sample color from an image or intermediate color from a gradient

Alt + Shift-click + Live Paint Selection tool

Option + Shift-click + Live Paint Selection tool

Add to/subtract from a selection

Shift-click + Live Paint Selection tool

Shift-click + Live Paint Selection tool

Select all connected faces /edges with same fill/stroke

Double-click + Live Paint Selection tool

Double-click + Live Paint Selection tool

Select all faces/edges with same fill/stroke

Triple-click + Live Paint Selection tool

Triple-click + Live Paint Selection tool