Classifying fusion categories is a problem that at the moment seems out of reach, since it includes the classification of finite groups and semisimple Hopf algebras. However, a lot of efforts have been made in classifying "small" fusion categories. Small can be interpreted in different ways, such as small rank, having a generator with small dimension, or having a global Frobenius-Perron dimension with few prime divisors. In this talk, we will give an overview of the classification program of certain notions of small fusion categories and we will mention some recent results about classification of odd-dimensional modular and fusion categories.
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