The chapter presents the results of research aimed at primary school pupils and their problems in solving word problems. Based on clinical interviews with pupils over solutions of different traditional and non-traditional word problems tasks of different difficulty we found following problems: (1) text comprehension and grasping of word problems (language barriers, comprehension of the mathematical structure of the task mathematization - convert text into the language of mathematics), (2) solving of inconsistent word problems (language is inconsistent with arithmetic operations) and compared word problems, (3) multi-step tasks and (4) technical part of solving word problems (numerical errors and errors in algorithms). The research also revealed significant problems with pupils modeling and creating functional notations and graphical representations of tasks (sketches, images, tables). Individual critical points are analyzed and commented in terms of possible causes and ways of correcting and putting in context with the results of many foreign and domestic research and comparative tests (TIMSS, PISA, CERMAT), including the results of an online questionnaire for teachers of 1st and 2nd degree created for this research needs. Critical points are illustrated with excerpts from interviews and written records of students solving processes.