Polymeric layers (50) comprising an array of blind openings (56) extending into the first major surface (52, 10111, 11211), but not through the second major surfaces (54, 10112, 11212). The blind openings each have a series of areas through the openings from the first major surface towards the second major surfaces ranging from minimum to maximum areas, where for at least a majority of the blind openings the minimum area is not at the first major surface. At least a portion of the first major surface comprises a first material and extends up to, but not into the second major surface. At least a portion of the second major surface comprises a second, different material. Methods for making the polymeric layers are also disclosed. Polymeric layers are useful, for example, as components in personal care garments such as diapers and feminine hygiene products. They can also be useful for filtering (including liquid filtering) and acoustic applications.