This is a report of excellent quality, which studies the global behavior of flat surfaces with singularities in Euclidean 3-space \(\mathbb R^3\). It successfully combines a survey of known results on complete flat surfaces, with a series of new results. The authors belong to a strong group of pioneering experts in this area. For the definition of a flat front and significant related research, one should consult several previous works by M. Umehara, K. Yamada and W. Rossman. On the other hand, the exposition is so clear and detailed, that the paper can be followed even without studying the previous literature. On short, the paper extends the notion of completeness to flat fronts. It also provides a representation formula for a flat front with complete immersed ends, and with a nonempty compact singular set. The applications and examples provided are extremely well chosen and of special significance.