Toric varieties are popular objects in algebraic geometry, as they can be modeled on polytopes and polyhedral fans. This is mainly because there is a dictionary between their geometric properties and the combinatorial invariants of their polytopes. This dictionary can be extended from toric varieties to arbitrary varieties through toric degenerations. In this talk, I will first recall the notion of toric degenerations which generalizes the fruitful correspondence between toric varieties and polytopes to arbitrary varieties. Then I will show some prototypic examples of toric degenerations (of Grassmannians) which are related to Young tableaux and Gelfand-Cetlin polytopes. I will describe how to obtain such degenerations using the theory of Gröbner fans and tropical geometry, and show the relations among their associated Newton-Okounkov bodies.