RO systems push water under pressure through a semipermeable membrane to allow the good part of water through and the bad part to stay in the input side and be washed away. Typical systems will operate with an efficiency of 4:1 or 5:1 meaning that four or five gallons of water go into the unit to produce each one gallon of filtered water. The rest of the water washes through the unit and goes into the drain. (This ratio can be worst for many older units whilst there are some manufacturers now advertising RO units with much lower waste).
My experience with RO systems is that they work well at producing clean drinking water. The initial equipment cost can be quite high as compared to a typical cartridge water filter system. But once that initial cost is past you there can be a quite long operational period without additional regular maintenance costs - that is unless the RO installation uses some post carbon filters which do require some maintenance.
The storage/filter tank that is part of an RO system can have problems however and if that happens replacing that part of the system can be a substantial cost. They can develop problems with the membrane or bladder inside the tank. There can also be problems with bacteria contamination in an RO system if it is not used properly. The manufacturer should provide instructions for their unit so that it is installed properly and kept serviced if necessary.
There are some health considerations with RO units in that they remove more things from water than just harmful things. Many of the beneficial minerals in the water are also removed by these units and there are arguments out there that this can be harmful in the long run if all the water you drink comes from an RO unit. As a matter of fact some commercial bottled water companies that produce their water via industrial scale RO systems are known to re-mineralize the filtered water to bring back some of its taste and benefits.