In this review, a brief introduction is given to the development of acoustic superlens cloaks that allow the cloaked object to receive signals while its presence is not sensed by the surrounding, which can be regarded as “cloaking an acoustic sensor”. Remarkably, the designed cloak consists of single-negative materials with parameters independent of the background medium or the sensor system, which is proven to be a magnifying superlens. This has facilitated significantly the design and fabrication of acoustic cloaks that generally require double-negative materials with customized parameters. Such innovative design has then been simplified further as a multi-layered structure comprising of two alternately arranged complementary media with homogeneous isotropic single-negative materials. Based on this, a scattering analyses method is developed for the numerical simulation of such multi-layered cloak structures, which may serve as an efficient approach for the investigation on such devices.