Models were quite neglected by philosophers of science and even scientists before the second half of 20th century: science was more thought of as in the business of producing statements about the world, but the view was criticised in particular by Suppes and Suppe in the 60's and 70's, who emphasised the central role of models in scientific representation and empirical confrontation.
This has come to be called the semantic view of theories, according to which a scientific theory is just (or is better presented through, analysed as...) a collection of models, and it as been endorsed by many authors, realist or anti-realist alike (e.g. van Fraassen, French, Ladyman, ...).
Models are conceived of by these authors as mathematical structures that represent features of the world, and the laws of a theory are just a way to describe this collection of structure.
These authors think that this view has several vitues: it is close from scientific practice, where empirical confrontation is made through comparison of data models and theoretical models (e.g. van Fraassen "the scientific image"), mathematical structures are more or less language-independent which allows one to bypass semantic issues in science (ibid), it provides mathematical tools such as isomorphisms to analyse intertheoretical relations (reduction, theory change), etc.
Not everyone agrees though: some think that theoretical laws are more than descriptions of collections of models (but represent natural laws, e.g. Maudlin in "metaphysics within physics"), or should be viewed as tools to produce contextual models (Cartwright, Suarez). Some think that language is still important to apply models (Chakravartty). But in any case, the importance of models in scientific activity is widely recognised today.
For a review of this specific debate you can read Lutz "what was the syntax-semantic debate about?" Or SEP entry on the structure of scientific theories
Note however that "model"is a polysemic word. I only addressed one aspect here: models as mathematical structures built from theoretical laws. There are other types of models: scale models (a reproduction of DNA), analogies and metaphors (model of the mind as a computer) or thought experiments... And a large literature on their status and role.
For a larger view on models in general you can read the dedicated SEP https://plato.stanford.edu/entries/models-science/ or Bailer-Jones "scientific models in philosophy of science".