Cabbage aphids have good camouflage, and may not be seen until they have become quite numerous. In addition to the aphids themselves, look for black deposits of honeydew where the aphids have been feeding. Late-maturing Brussels sprouts and cabbage are at high risk for damage by cabbage aphids.
Pull up and compost old plants, because cabbage aphids can overwinter in dead plant tissue. Clip off and compost stems holding aphid clusters. Harvest Brussels sprouts often, because sprouts left too long can serve as aphid nurseries. Encourage beneficial insects including lady beetles, syphid flies, and lacewings, which are important aphid predators.
In small outbreaks, a high pressure spray from the garden hose can help remove cabbage aphids from plants. Follow up with two applications of insecticidal soap, one week apart. Be sure to apply the soap spray to leaf undersides and crevices.
Lady beetles and their larvae are great beneficial insects to welcome into your garden. Ants tend to be attracted to the honeydew left by aphids, so ant activity can often lead you to aphid colonies.