David Turnbull's experiments and theoretical insights paved the way for much of our modern understanding of phase transitions in materials. In recognition of his contributions, this lecture will concentrate on phase transitions in a material system not considered by Turnbull, thin diblock copolymer films. Well-ordered block copolymer films are attracting increasing interest as we attempt to extend photolithography to smaller dimensions. In the case of diblock copolymer spheres, an ordered monolayer is hexagonal, but the ordered bulk is body-centered cubic (bcc). There is no hexagonal plane in the bcc structure, so a phase transition must occur as n, the number of layers of spheres in the film, increases. How this phase transition occurs with nand how it can be manipulated is the subject of the first part of my presentation. In the second part of the talk, I show that monolayers of diblock copolymer spheres and cylinders undergo order-to-disorder transitions that differ greatly from those of the bulk. These ordered 2D monolayers are susceptible to phonon-generated disorder as well as to thermal generation of defects, such as dislocations, which, while they are line defects in 3D, are point defects in 2D. The results are compared to the theories of melting of 2D crystals (spheres) and of 2D smectic liquid crystals (cylinders), a comparison that will allow us to understand most, but not all, of the features of these order-disorder transitions that occur as the temperature is increased.