The grandstands of La Zarzuela Racecourse in Madrid designed by the engineer E. Torroja and the architects C. Arniches and M. Dominguez are one of the world's most outstanding concrete constructions of the first half of the 20th century. This paper describes the design competition and the conceptual design process that led to their construction and carries out a critical assessment of the grandstands from the perspective of Structural Art. By doing so, the paper helps to develop the discipline of structural criticism, and points out lessons learned from their design and construction process which should not be forgotten at the present time, such as: (a) the importance of design competitions; (b) the fact that the pursuit of economy and efficiency can actually improve the quality and aesthetics of the design; (c) the importance of combining logical reasoning based on technical criteria with imagination to achieve excellence in structural design; and (d) the importance of estimating structural behavior by simple formulas and of learning from both existing structures and experimental models.