Seismic methods are used in a wide variety of contexts to investigate subsurface Earth structures, and to explore and monitor resources and waste-storage reservoirs in the upper ~100 km of the Earth's subsurface. Reverse-time migration (RTM) is one widely used seismic method which constructs high-frequency images of subsurface structures. Unfortunately, RTM has certain disadvantages shared with other conventional single-scattering-based methods, such as not being able to correctly migrate multiply scattered arrivals. In principle, the recently developed Marchenko methods can be used to migrate all orders of multiples correctly. In practice however, using Marchenko methods are costlier to compute than RTM-for a single imaging location, the cost of performing the Marchenko method is several times that of standard RTM, and performing RTM itself requires dedicated use of some of the largest computers in the world for individual data sets. A different imaging strategy is therefore required. We propose a new set of imaging methods which use so-called focusing functions to obtain images with few artifacts from multiply scattered waves, while greatly reducing the number of points across the image at which the Marchenko method need be applied. Focusing functions are outputs of the Marchenko scheme: they are solutions of wave equations that focus in time and space at particular surface or subsurface locations. However, they are mathematical rather than physical entities, being defined only in reference media that equal to the true Earth above their focusing depths but are homogeneous below. Here, we use these focusing functions as virtual source/receiver surface seismic surveys, the upgoing focusing function being the virtual received wavefield that is created when the downgoing focusing function acts as a spatially distributed source. These source/receiver wavefields are used in three imaging schemes: one allows specific individual reflectors to be selected and imaged. The other two schemes provide either targeted or complete images with distinct advantages over current RTM methods, such as fewer artifacts and artifacts that occur in different locations. The latter property allows the recently published 'combined imaging' method to remove almost all artifacts. We show several examples to demonstrate the methods: acoustic 1-D and 2-D synthetic examples, and a 2-D line from an ocean bottom cable field data set. We discuss an extension to elastic media, which is illustrated by a 1.5-D elastic synthetic example.