Consider 4-space with its standard symplectic structure. Then consider two curves in parallel hyperplanes of this space. A natural question is whether there exists a Lagrangian cobordism between these curves. I will discuss how Lagrangian cobordisms can be non-symmetric: there are cases where there does exist a Lagrangian cobordism between the curves but not if the heights of the curves are interchanged. I will also describe how when given a Lagrangian disk in 4-space with its boundary contained in a hyperplane, the shape of the boundary determines the minimum size of a rectangular cylinder that contains the disk. These obstructions to the existence and squeezing of Lagrangian cobordisms come from a notion of capacities defined through the theory of generating families.