The article discusses how modern complex data challenges traditional statistical methods. The researchers propose using pseudo-likelihoods, specifically composite likelihood functions, to address these challenges. They focus on three main issues: the distribution of log likelihood ratios, the accuracy of test statistics, and the robustness of estimators. They introduce new methods like the empirical log likelihood ratio test statistic and the non-parametric saddlepoint test statistic to improve accuracy and robustness in statistical inference.