What pests and diseases are a threat to chestnuts?

Chestnut trees are susceptible to a few pests such as the chestnut weevil, oriental chestnut gall wasp, spider mites, shot hole borers, filbert worms, and even deer and squirrels.

Diseases of concern include chestnut blight, as well as alternaria, aspergillus, botrytis, fusarium, penicillium, phomopsis, phytophthora root rot (also known as ink disease), leaf spot, powdery mildew, and oak root fungus. Asian chestnuts are particularly susceptible to twig canker.

Source:

Planting and growing chestnut trees 

Chestnuts