Menstrual cups are a step up from this!

They produce much less waste, are much less messy (almost never leak), and don't need to be changed as often (once every 6 - 12 hours and without the TSS risks that tampons have).

It's better to use running water to wash them out, but simply wiping them with tissue paper can work too (albeit a little messily), if water is scarce.

A downside that I've read about however is that just like with tampons, some cultures consider inserting anything into the vagina as losing your virginity so using them may be considered taboo.