Linked from
The 5 pages that link to Vinogradov's theorem, each with the reason it gives.
Circle methodBroader topic: Vinogradov established this result by controlling major and minor arcs.
Exponential sumBroader topic: Its proof uses estimates for exponential sums over primes.
Waring's problemRelated: Its methods and questions resemble those used for sums of powers.
Goldbach–Euler theoremRelated: It is a major proved result for the related three-prime problem.