Aquarium algae is a symptom of excess nutrients. The most important thing is to fix that imbalance with filtration, water changes, clean up crew, etc. However, aquarium algae, like green hair algae or red slime algae (technically, cyanobacteria is not algae), can quickly spread and harm corals. A fish tank algae remover can help while you work on the imbalance. An algae remover should be used in combination with manual removal and improved maintenance for the best long term results.
For non-chemical algae solutions, check out algae reactors and refugiums, which intentionally grow algae in controlled environments to reduce algae in the display tank.