  The concept of depth has proved very important for multivariate and
functional data analysis, as it essentially acts as a surrogate for the notion
a ranking of observations which is absent in more than one dimension. Motivated
by the rapid development of technology, in particular the advent of `Big Data',
we extend here that concept to general metric spaces, propose a natural depth
measure and explore its properties as a statistical depth function. Working in
a general metric space allows the depth to be tailored to the data at hand and
to the ultimate goal of the analysis, a very desirable property given the
polymorphic nature of modern data sets. This flexibility is thoroughly
illustrated by several real data analyses.
