This chapter provides the definition of normalized quantile residuals; and other diagnostic tools based on residuals, such as worm plots and Q statistics. The proper use of diagnostics is important because it reveals the strengths and weaknesses of a model. The chapter aims to understanding the tools for checking the adequacy of a Generalized additive models for location scale and shape (GAMLSS) model. The use of diagnostics is an important step in model checking and hence model selection. The chapter introduces normalized quantile residuals for a continuous response variable and normalized randomizedquantile residuals for a discrete response variable. It describes the plot() function of gamlss and the detrended transformed Owen's plot, which provides a method for visually checking the adequacy of a fitted model. The main advantage of normalized quantile residuals is that, whatever the distribution of the response variable, the true residuals always have a standard normal distribution when the assumed model is correct.