Flutter Layouts are built using widgets, which include both visible elements like images, icons, and text, as well as invisible elements like rows, columns, and grids that arrange and align these visible widgets.  Flutter allows for building complex layouts by composing multiple widgets. An example is a layout with three icons and labels, where each icon and label is contained within a column, and the three columns are arranged in a row.  The Container widget provides customization options for child widgets, such as adding borders, padding, margins, background colors, and more.  In the example, the text widget is placed within a container to add margins, and the entire row is also within a container for additional margin and padding. The overall UI is further controlled by properties like color and text style.