Novel types of percolation have been develped to better understand the structure and improve the function of complex networks. We will show how the k-core percolation can yield useful information about the topology of complex networks. We will discuss a percolation model that considers path length restrictions (Limited Path Percolation (LPP)) which are relevant for information flow and epidemics. Another percolation process (Equal Graph Partitioning (EGP)) which is characterized by fragmenting the network into equal size clusters and results in removing or immunizing minimal number of nodes, will be also discussed. The EGP model is useful for developing efficient immunization strategies.