One thing I think is important to realize is that just sampling over the area of a light source isn't always a cure-all depending how big that area is, the characteristics of the light, and the characteristics of the surface. For example, a large area light over a glossy surface can be difficult to model just by sampling the light's area: In these cases, you can use multi-importance sampling to capture opposing effects simultaneously. Here's a good document covering both the math behind and the usefulness of multi-importance sampling: https://graphics.stanford.edu/courses/cs348b-03/papers/veach-chapter9.pdf
One thing I think is important to realize is that just sampling over the area of a light source isn't always a cure-all depending how big that area is, the characteristics of the light, and the characteristics of the surface. For example, a large area light over a glossy surface can be difficult to model just by sampling the light's area: In these cases, you can use multi-importance sampling to capture opposing effects simultaneously. Here's a good document covering both the math behind and the usefulness of multi-importance sampling: https://graphics.stanford.edu/courses/cs348b-03/papers/veach-chapter9.pdf