Novikov–Boone theorem and Novikov–Adian theorem: Consequences

There are two famous results related to the name of Piotr Sergeevich Novikov. The first one, known as the Novikov-Boone theorem, asserts the existence of a finitely presented group with unsolvable word problem. The second one, elaborated jointly with S. I. Adian, states that the free Burnside group of odd exponent $n \ge 4381$ with at least two generators is infinite. The both results are of fundamental nature and have a great influence on further mathematical research. In my talk I will present a small historical part and give a survey on some results stemmed from the two theorems including recent developments.