Climbers
There is a limited range of climbing plants that fit into the exotic garden easily - certainly not many unusual ones. Here are some I think are appropriate.
ACTINIDIA
AMPELOPSIS
AKEBIA
ARISTOLOCHIA
CAMPSIS
CISSUS
CLEMATIS
ECCREMOCARPUS
HEDERA
HOLBOELLIA
HUMULUS
LAPAGERIA
LARDIZABALA
LONICERA
MANDEVILLA
MUTISIA
PANDOREA
PARTHENOCISSUS
PASSIFLORA
PILEOSTEGIA
SCHIZOPHRAGMA
STAUNTONIA
TRACHELOSPERMUM
VITIS