Pleated blinds

Pleated blinds are shades made from a pleated fabric (which helps to add texture to a room) that pull up to sit flat at the top of a window to hide from sight when open.

Honeycomb pleated blinds, or cellular blinds (actually cellular shades) are similar to pleated blinds except that they are made up of two or more layers joined at the pleats to form 'cellular' compartments that trap air, providing insulation. Due to their cellular construction, cellular blinds (aka energy saver) are known to the energy conscious as one of the highest energy-efficient and sound-absorbent blinds of any window treatment. For greater insulation, cellular blinds are available in a variety of cell sizes, including 3/8" single cell, 3/4" single cell, 3/8" double cell and even triple cell. The more cells, the greater energy efficiency.

One disadvantage with these cellular pleated blinds is that small insects crawl into the hollow chambers and die. Removing them is not easy.

All of the above can also be motorized, which is a great option for safety in homes with children and/or pets.

...
Wikipedia