The coupling in a directional coupler (DC) has attracted lots of attention as a basic block for photonic integrated circuits. Most of previous work was focused on symmetric DCs consisting of two identical optical waveguides. In this case light power can be transferred from one waveguide to the other one completely when choosing the length L of the coupling region appropriately. Recently, an asymmetric DC (ADC) consisting of non-identical waveguides in the coupling region has been attracting more and more attention because of the versatility for various useful applications. ADCs can be formed by combining two ore more waveguides with different dimensions, shapes as well as bending radii for the core regions. In particular, silicon nanophotonics developed in the recent years provides a very good platform to make ADCs very useful and interesting. In this paper, we give a review for recent progresses of versatile ADCs on silicon, including the following three parts: (1) ADCs for power splitter used in microring resonators and Mach-Zehnder interferometers; (2) ADCs for realizing ultracompact and broadband PBSs; (3) ADCs for realizing mode (de)multiplexers.