One-sided discretization inequalities and sampling recovery

Recently, in a number of papers it was understood that results on sampling discretization and on the universal sampling discretization can be successfully used in the problem of sampling recovery. Moreover, it turns out that it is sufficient to only have a one-sided discretization inequality for some of those applications. This motivates us to write the present paper as a survey/research paper with the focus on the one-sided discretization inequalities and their applications in the sampling recovery. In this sense the paper complements the two existing survey papers on sampling discretization.