This is the Neato XV-11 robotic vacuum cleaner, which retails for around $400 at Amazon. There is a small but fairly powerful vacuum in its front, and the robot moves around while the vacuum sweeps up dirt as it moves. It navigates a room using a small laser that rotates rapidly in the "turret" in the back, using the input it gets to avoid objects. It does a good job of this, and rarely bumps into our furniture. You can also block off areas using magnetic strips, included with the product. Dust and dirt is collected in a bin in the front of the robot, which should be emptied after each use. We normally get a full bin of cat hair, dust, etc. with each run, and it takes a little under an hour to do four rooms. There's an option to have the robot run remotely on a set schedule, but I prefer to be here when I do run it, as occasionally it will run into an obstacle it needs some help getting around - not often, but sometimes. The robot will return to its base station automatically to recharge, and recent software upgrades have noticeably improved its ability to remember its previous path and complete this successfully. One bonus is that the robot can get under beds and furniture which we were vacuuming infrequently with the manual vacuum. The flipside to being good at avoiding furniture is that every few months you will need to manually vacuum in edges and corners, since the collision avoidance software and design doesn't allow the robot to clean those very well.
One downside: we had to return our first model because of a continuing problem with "RPS errors". This is basically a problem with dust getting into the turret sensors . It can be prevented by blowing the turret with compressed air before each use, and the model we received from Neato in exchange has rarely had this problem, so they seem to have solved or at least limited the issue. A more popular robot vacuum is the Roomba in its various models, but I chose not to go with that after reading many reviews that all Roombas models had problems with the front brushes (there to push dirt into the vacuum) regularly snapping off and having to be replaced.
This is the Mint 4200 series robot cleaner, which retails for $200 at Amazon. We use this for cleaning our house's hardwood and kitchen floors. You place either a "dry" or "damp" cloth shammy on to the front of the robot; both come with the product, or you can use Swiffer sheets also. It navigates by exchanging information with a base unit which projects an invisible beam up on to the ceiling of whatever room is being cleaned. The robot builds a "map" of the room by moving around until it bumps into something, which it then stores and knows not to try moving into that space again. This actually works better than it sounds, and the system is fairly efficient at this. Normally every time we run the Mint on our floors, it finishes after about an hour with a lot of dirt and pet hair collected. The shammies can be cleaned in with the normal laundry, though I recommend brushing off the major dirt before putting it in with the rest of the wash. As with the Neato, a good function is that it gets under furniture and into spaces which we normally wouldn't remember to clean regularly.
In all, we're quite happy with both. There's a learning curve to each, but they've both saved a lot of time and have cut down on the amount of weekly housekeeping we have to do. In both cases I can now set up each robot, push "start", and simply let it run mostly without assistance, and after about an hour the cleaning is done. That's about all one could ask for from a robotic assistant. Oh, and they're fairly neat to watch as they roll around cleaning and going around anything that gets in their way. There's also robots available for lawn mowing, but the price (over $1,500) is prohibitive right now. The makers of the Roomba also have models for floor cleaning, pool cleaning, and gutter cleaning. As with anything, caveat emptor: read the reviews on Amazon,com and elsewhere before purchasing.