Order related procedures (such as median, quantiles, and nonparametric procedures) in one-dimensional data analysis and inference have played such important roles that their analogues in high dimensions have been sought for years (but without many satisfactory results). The task is non-trivial because there is no natural and clear order principle in high dimensions. On the other hand, data depth turns out to be a quite promising tool for a center-outward ordering of multi-dimensional observations. In this talk motivations of data depth are discussed. Examples illustrating notions of data depth including half-space, simplicial and projection depth are provided. Applications of data depth in location, in regression, and in other settings are discussed. Depth based procedures can outperform their competitors by maintaining a good balance between efficiency and robustness. Computing issues and some future research directions of data depth are briefly addressed.