The plant is Rhoicissus rhomboidea 'Ellen Danica', common name Mermaid Vine, though its often referred to as grape ivy. At first glance, rust infection springs to mind, but a closer examination reveals what are apparently eggs or crawlers. I can't decide whether it's an aphid infestation or soft scale/mealybug, or both, but I'm inclining to the soft scale, so its not a fungal infection, but insect invasion. You can either use a heavy duty systemic insecticide which treats for mealybug, scale and aphids (they usually cover aphids as well) or try spraying with neem, weekly - if you choose the latter route, it may mean reapplying weekly for some period of time. When you spray, be sure to cover both the backs and tops of leaves, as well as the stems. If you choose the systemic insecticide treatment, take the plant outdoors and spray outside, then when it stops dripping, bring it back indoors.
If the plant is large with plenty of foliage, then cutting it back by half or a third will dispose of some - these plants do not mind being cut back, so it will recover.
In response to your comment below - typical of scale if the objects cannot be wiped away easily - scale come in different forms and have a crawler stage and a fixed and immovable stage, sometimes with the two going on together. It is a little unusual to find them or their 'cotton' deposited on the tops of the leaves, they usually stick to the backs, which is why I thought the deposits on the front might be eggs or whitefly. Doesn't change the treatment recommended in the first part of this answer though. More general info https://www.planetnatural.com/pest-problem-solver/houseplant-pests/scale-control/