Embryological Evolution
An embryo goes through a number of stages before it develops into a fetus and eventually into a living offspring. Studying the structures that develop during an embryo's various stages of growth is called embryology and can be used to show the genetic similarities that suggest certain patterns of evolution.
Most embryos look similar in their early stages, but as they develop, the differences between species become more obvious. Embryos of organisms that have a closer genetic relationship to one another tend to look similar for a longer period of time since they share a more recent common ancestor.
In early embryonic stages, embryos will often form structures that will not be present in the organism's final form.
For example, human embryos develop a tail in the beginning stages of our development. However, further along in the process, certain genes kick in that absorb the tail cells, leaving us with a nub referred to as a vestigial tail. The development of this vestigial tail suggests that we had a tail at some point in our evolutionary history, but adaptations and evolutionary shifts made tails unnecessary for our survival.
Historic Theories
Early on, a major player in the progression of embryology was a German scientist named Ernst Haeckel. While studying vertebrate embryos, he came up with many (exaggerated) drawings to illustrate the biogenetic law (recapitulation theory). This was a theory stating that "ontogeny recapitulates phylogeny". In much simpler terms, this means embryos develop in a way that mirrors how their ancestors evolved over time.
Although this hypothesis was proven to be incorrect, it was still a major influential idea of the 18th century.