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In 1959 Kolmogorov and Sinai introduced entropy for measureÌýpreserving transformations of a probability space, generalizing theÌýnotion from statistical mechanics and information theory. TheirÌýdefinition can be naturally extended to measure preserving actions ofÌýamenable groups, groups which one can average over in a suitableÌýsense. On non-amenable groups, e.g. the free group with at least twoÌýgenerators, this definition breaks down. In fact an example ofÌýOrnstein and Weiss from 1987 cast doubt on whether a useful notion ofÌýentropy could be defined beyond amenable groups. However in 2010 LewisÌýBowen developed an entropy theory for actions of a class of groupsÌýcalled sofic groups, which properly include amenable groups. In thisÌýtalk I will first discuss the classical theory of entropy and itsÌý various interpretations, then compare it to sofic entropy. TimeÌýpermitting I'll mention some open problems in the area and connectionsÌýto other areas like operator algebras. Focus will be put on specificÌýexamples and developing intuition. No knowledge beyond basic analysisÌýwill be assumed.