V. Kac classified finite dimensional simple Lie superalgebras over the field of complex numbers in 1970s. They constitute several series and are divided into two types based on their even part: classical type and Cartan type. Lie superalgebras of Cartan type consists of four series W (n), S(n), S (n), and H(n). In this talk I will briefly introduce Cartan type Lie superalgebras and then I will show how explicitly one can compute cohomology and support varieties for W (n) and S(n). I will also mention what we have for H(n) and present a new theorem on realizability of support varieties that holds both for classical and Cartan type Lie superalgebras. If I have time I am planning to present some open problems at the end of my talk. The results about W (n) represents joint work with Jonathan Kujawa and Daniel Nakano.