When to use Their, There and They're.

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No real need to confuse these.  'Where are they?' ' They're there, their eyes shining bright with curiosity.'
Their:  the possessive form of they, as 'your' is the possessive form of 'you'. 'The politicians conned their constituents, as usual.'
There: in that place, at that point. 'Over there is the statue of the Venus de Milo.'
They're: contraction of they are. 'You can't trust leaders; they're all suffering from personality disorders.'