For 35 years I have been a weaver of seats made mostly of cane and wicker/reed.  In short these materials come from basicaly the same plant -- BAMBOO.  Bamboo grows in areas that have high humidity most of the time.  When we harvest it to use for furniture we don't take that into account. 

All bamboo, cane, wicker should be given a good rain bath at least twice a year.  If it is a seat in a wood chair you may need to take the finish into consideration.  In this instance think of the seat like you would your house plants.  They need water -- your seats need moisture.  Many people used to oil the seat along with the rest of the wood.  The problem with that is that the oil does not penetrate completely and can stain fabrics when you sit down.  I have found the best way to solve this problem is to MIST.  Plain water is good but water and fabric softener mixed half and half is better.  Mist once a month at least but if you live in an area where you have forced air heat in the cold months then mist once a week. 

Old material can benefit as well as a newly woven piece.  Wicker that is kept indoors year round can be taken outside and given a gentle power wash.  Even paper wicker can be washed just don't get up too close. 

If you have painted pieces and you want to repaint be sure to use oil or water based finished.  Alchol based finishes will only dry the material out and cause it to crack and break. 

This information can be applied to old and new baskets for those of you that collect them also.