I almost returned this because it wouldn't turn on and I thought it was defective (supported by other reviews saying the same). Turns out that for some reason, it wasn't compatible with the charging cable I was using. Switching cables, including the one it came with, solved the issue. A green light will turn on inside the lamp to let you know it's charging.
The light has 16 discrete color options, a continuous RGB cycle mode, rechargeable battery, touch button (which can do everything the remote can except for brightness adjustment, as far as I can tell), and despite its small (3.5"x4") size, outputs enough light to illuminate an at least 9x12 ft room with a 9 ft ceiling (from the top of a 2.5 ft desk - see attached video).
Couple quirks I've noticed: changing the brightness of the lamp also changes the speed of the water effect (brighter=faster). As far as I can tell, there is no way to separate the two. It also doesn't appear to be possible to change the brightness of the RGB cycle mode.
While I could nitpick about these quirks or the fact that the touch button doesn't cycle the colors in an intuitive way (goes in order of the colors on the remote from left to right instead of top to bottom), this product does exactly what I wanted at the lowest price I found, and for that, it gets five stars.