In the talk I will give an overview of the material I included in the master course "Statisticsl inference for high dimensional data". The talk has two parts: multiple testing and classification. The "high dimension" in the title refers to situations where each observation has in the order of 1000 variables or more, and at the same  time the sample size is small, in the order, say, from 20 to 100. For the multiple testing situation the point is to allow false positives, and then try to make a control of how many false positives that are present. In the classification situation a limiting situation is considered where the dimension $m$ is much larger than the sample size  $n$, but $\log(m)/n\rightarrow 0$. Positive results for the thresholded  independence classifier are mentioned and a discussion of the imbalance problem is given. The latter refers to the situation with two groups and the number of observations from the two groups differ.