The overall aim of education is to train proactive, motivated, and independent citizens to face and overcome continuous challenges. Critical thinking—finding solutions to problems—is of primary importance in the 21st century to handle challenging situations and deal with obstacles in careers. A critical literature review approach was used to assess, critique, synthesizes, and expand the theoretical foundation of the topic. Teaching mathematical problem-solving is an efficient way to develop 21st-century skills and to give cross-curricular experiences with real-world meaning to learners. Concrete examples were presented to prove that Pólya’s heuristic could be used in a broader context to help learners acquire the modern skills needed to succeed in their careers. By including in the learning process and practicing specific methods for solving mathematical problems, students could learn a way of thinking to approach and solve problems successfully in a broader context in life. The paper’s outcome provides teachers and educators with methods, learning models, and strategies for developing 21st-century skills in students at all levels during classroom activities.