PhD thesis in Computer Science focused on Natural Language Processing, written by Simona Frenda under the supervision of Prof. Viviana Patti and Prof. Paolo Rosso. This thesis was developed in a co-tutelle program between the PRHLT Research Center of the Universitat Polit`ecnica de Val`encia (Spain) and the Computer Science Department of the University of Turin (Italy). In this work, we analysed, linguistically and computationally, the characteristics of the implicit abusive language, especially when it is masked as sarcastic. The thesis defence was held in Torino on June 6th, 2022. The doctoral committee was composed by: Prof. Liviu Petrisor Dinu (University of Bucharest, Romania), Prof. Els Lefever (Ghent University, Belgium) and Prof. Elena Cabrio (Universit´e Cˆote d’Azur, France). An international mention was achieved, and the work was graded as excellent and awarded Cum Laude.