This volume collects selected, peer-reviewed contributions from the 2nd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Cadiz (Spain) between June 11-16 2014, and sponsored by the American Statistical Association, the Institute of Mathematical Statistics, the Bernoulli Society for Mathematical Statistics and Probability, the Journal of Nonparametric Statistics and Universidad Carlos III de Madrid. The 15 articles are a representative sample of the 336 contributed papers presented at the conference. They cover topics such as high-dimensional data modelling, inference for stochastic processes and for dependent data, nonparametric and goodness-of-fit testing, nonparametric curve estimation, object-oriented data analysis, and semiparametric inference. The aim of the ISNPS 2014 conference was to bring together recent advances and trends in several areas of nonparametric statistics in order to facilitate the exchange of research ideas, promote collaboration among researchers from around the globe, and contribute to the further development of the field.