Differential Galois groups are algebraic groups that describe symmetries of some systems of differential equations. The solutions considered can live in any differential field and thus a natural framework to consider such symmetries is the setting of differentially closed fields. I will describe this setting and sketch the proof of the fundamental theorem of differential Galois theory using it. If time permits, I will mention Kolchin's geometric approach to study differential equations, and Hrushovski-Sokolovic classification of strongly minimal differential equations (building blocks of all differential equations in differentially closed fields).