  This work is a survey of the most relevant background material to motivate
and understand the construction and classification of translating solutions to
mean curvature flow on a family of solvmanifolds.
  We introduce the mean curvature flow and some known results in the field. In
particular we explore the notion of translating solution in the Euclidean space
and extensions into other Riemannian manifolds. We also include a discussion on
solvmanifolds and some elements of its geometry that are relevant to our work.
  We finish by posing the equations that describe translating solutions to mean
curvature flow on our family of 3-dimensional solvmanifolds with some
additional assumptions.
  This project emerged at the ``Latin American and Caribbean Workshop on
Mathematics and Gender'' held at Casa Matem\'atica Oaxaca (CMO) from May 15-20,
2022.
