To characterize the family of learnable classes in the setup of binary valued classification with the zero-one loss, Vladimir Vapnik and Alexey Chervonenkis coined the combinatorial measure called the Vapnik-Chervonenkis dimension (VC dimension) in 1970. In this talk, I will introduce the concept of VC dimension and show several examples as well as the fundamental theorem of statistical learning. Then I shall present our work in this field, we show that every concept class induced by a discrete Markov network has a labeled sample compression scheme of size equals to its VC dimension d, that is, we provide a partial positive answer to the Sample Compression Conjecture. Finally, I introduce some advances related to VC dimension.