Late blight
Agent: Phytophthora infestans

Symptoms
Dark green or black spots appear and spread on the edges of the leaves. The same can appear on the fruits.
Control and prevention
Remove affected parts. Prevention: drip irrigation, good ventilation, not too much humidity, resistant varieties. If attacked - fungicides.
Related problems
Similar symptoms might indicate a different cause — compare them.

Early blight and black fruit rot
Alternaria solani
Usually appears when fruits begin to set. First affects the lower leaves, then the stem and fruits. Large brown or black spots with concentric rings appear on them. Around the spot, the leaf begins to yellow and dies. It also attacks potatoes and eggplants. The fungus is resistant and persists for several years.

Mold
Symptoms caused by various fungi. Mold only survives in high humidity.

Septoria Leaf Spot
Septoria lycopersici
Forms light spots with dark edges, with black dots inside. Later the leaf yellows and falls off. Does not affect fruits. The fungus is resistant, survives winter.