What plants are suitable for around a pool?

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There are plenty of salt-tolerant plants, including many Australian natives that cope with coastal conditions. Consider a coastal banksia, dianella (flax lilies) or westringia (coastal rosemary). Some grevillea and fuchsia varieties might also suit. I also like agave and aloe plants, which can cope with anything.

Make sure you steer well clear of bamboo - they often cause issues with plumbing and paving. - Kermit

Hydrangeas are pretty tough and low maintenance. I think these blue hydrangeas look fantastic. - AndreaNg

Succulents are a great option given their lack of falling leaves, etc. I don't know about their salt tolerance, though. I've started popping some around my pool area but in places where they'll get little to no salt water splashing on them - so far, so good. - ProjectPete

The plants that have been mentioned by our members can be used near your chlorine pool as well. For example, the succulents are actually very tolerant of both salt and chlorinated water. Hydrangea macrophylla is also an excellent plant near the pool. My favourite one is the Westringia. It is drought tolerant and is excellent for hedging and screening. 

Chlorinated water or salt water is harmful to plants. I suggest that you water the plants with fresh water in case it has been splashed or drenched in pool water. - EricL