  A homogenizable structure $\mathcal{M}$ is a structure where we may add a
finite amount of new relational symbols to represent some $\emptyset-$definable
relations in order to make the structure homogeneous. In this article we will
divide the homogenizable structures into different classes which categorize
many known examples and show what makes each class important. We will show that
model completeness is vital for the relation between a structure and the
amalgamation bases of its age and give a necessary and sufficient condition for
an $\omega-$categorical model-complete structure to be homogenizable.
