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We present Las Vegas algorithms for constructive recognition and constructivemembership testing of the Ree groups 2G_2(q) = Ree(q), where q = 3^{2m + 1} forsome m > 0, in their natural representations of degree 7. The input is agenerating set X.  The constructive recognition algorithm is polynomial time given a discretelogarithm oracle. The constructive membership testing consists of apre-processing step, that only needs to be executed once for a given X, and amain step. The latter is polynomial time, and the former is polynomial timegiven a discrete logarithm oracle.  Implementations of the algorithms are available for the computer algebrasystem MAGMA.

Recognising the small Ree groups in their natural representations