Acclaimed fossil hunter Mary Anning (Kate Winslet) reminisches about how she found the fossils of a special sea lizard when she was 11 years old, which is now on display in a museum. One day a wealthy man walks into her shop and tells her his wife Charlotte Murchison (Saoirse Ronan) is unhappy and he wants Mary to take her to the shore every day to get her to take an interest in life. Mary can't say no after he offers her a large sum of money. Charlotte isn't keen on the idea either, admitting that she doesn’t like the water. However, she soon grows interested in the work, and especially interested in a romantic relationship with Mary.