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In this paper we survey recent developments over the last 25 years on themixed fractional moduli of smoothness of periodic functions from $L_p$,$1<p<\infty$. In particular, the paper includes monotonicity properties,equivalence and realization results, sharp Jackson, Marchaud, and Ul'yanovinequalities, interrelations between the moduli of smoothness, the Fouriercoefficients, and "angular" approximation. The sharpness of the resultspresented is discussed.

Mixed Moduli of Smoothness in $L_p$, $1