Ever since Amazon announced the Echo, the platform and Alexa's voice commands have been expanding and adding more partners and features. They haven't, however, gained the magical ability to control your house's manual window blinds. It has though become possible to connect Alexa to an Arduino board, which increases the potential uses for the platform.
An enterprising guy has used that to his advantage, MacGyvering his way into smart window blinds with an Arduino (he uses a SmartThings shield for his Arduino to connect it to the rest of his smart home system), a servo, and some lasercut gears. He details the whole process, which I'll be honest in saying I don't understand the first thing about, in an Imgur post that I'll link below. The end result of what seems to be a fairly simple(ish) installation is a set of three blinds that respond to his voice commands through Alexa.
It doesn't sound right to say, "Turn on/off the blinds," instead of, "Open/Close the blinds," and he jokes about it, but it seems to be a limit of Alexa's Arduino integration. Either way, it's so cool that we don't even care what the correct voice command should be.