Immunotherapy is the most promising therapeutic approach against malignant pleural mesothelioma (MPM). Despite technological progress, the number of targetable antigens or specific antibodies is limited, thus hindering the full potential of recent therapeutic interventions. All possibilities of finding new targeting molecules must be exploited. The specificity of targeting is guaranteed by the use of monoclonal antibodies, while fully human antibodies are preferred, as they are functional and generate no neutralizing antibodies. The aim of this review is to appraise the latest advances in screening methods dedicated to the identification and harnessing of fully human antibodies. The scope of identifying useful molecules proceeds along two avenues, i.e., through the antigen-first or binding-first approaches. The first relies on screening human antibody libraries or plasma from immunized transgenic mice or humans to isolate binders to specific antigens. The latter takes advantage of specific binding to tumor cells of antibodies present in phage display libraries or in responders' plasma samples without prior knowledge of the antigens. Additionally, next-generation sequencing analysis of B-cell receptor repertoire pre- and post-therapy in memory B-cells from responders allows for the identification of clones expanded and matured upon treatment. Human antibodies identified can be subsequently reformatted to generate a plethora of therapeutics like antibody-drug conjugates, immunotoxins, and advanced cell-therapeutics such as chimeric antigen receptor-transduced T-cells.