InAs nanowires (NWs) is a key material for high-speed electronics, near- and mid-infrared light emission and detection applications. Much effort has been devoted to the fabrication of InAs NWs and molecular beam epitaxy (MBE) evolved as a powerful method to grow semiconductor nanowires with several interesting features, but it was rarely reported. We present kinds of growths (metal-catalyzed growth, self-catalyzed growth, self-induced free-standing growth, self-induced position-controlled growth, self-assisted nucleation growth etc.) of InAs NWs by MBE, and discuss how to control growth of uniform-structure InAs NWs on homogeneous or heterogeneous substrates, which can provide the reference for the manufacture of low dimensional structure.