Random fields with isotropic increments were introduced by Kolmogorov in the 1940s. Gaussian random fields on N-dimensional Euclidean spaces with isotropic increments were classified as isotropic case and non-isotropic case by Yaglom in the 1950s. Such models were used widely in statistical physics. In particular, they were introduced to model a single particle in a random potential by Engel, Mezard and Parisi in 1990s. A basic question is to count the number of critical points (or local minima, saddles, etc.) of the fields, which is commonly known as complexity. In 2004, Fyodorov computed the large N limit of expected number of critical points for isotropic Gaussian random fields. However, the non-isotropic case creates new difficulty. In this talk, I will present some results on the large N behavior of complexity for this case. Connection to random matrices and large deviations will be explained. This talk is based on joint work with Antonio Auffinger (Northwestern University).