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The ability to synthesize recordings from surface data as if they had come from subsurface sources has allowed geophysicists to estimate subsurface properties. Either in the form of classical seismic migration which creates structural maps of the subsurface, to the more recent seismic interferometry which turns seismic sources into receivers and vice-versa, this ability has provided a rich trove of methods with which to probe the Earth's interior. While powerful, both of these techniques suffer from well-known issues. Standard migration requires data without multiply-scattered waves (multiples). Seismic interferometry, on the other hand, can be applied to full recorded data (containing multiples and other wave types), but requires sources (receivers) to be physically placed at the location from (to) one wishes to estimate responses. The Marchenko method, developed recently for the seismic setting, circumvents both of these restrictions: it creates responses from virtual subsurface sources as if measured at the surface. It requires only single-sided surface data, and a smooth estimate of the subsurface velocities. Initially developed for acoustic media, this thesis contributes the first elastic formulation of the Marchenko method, providing a more suitable setting for applications for the solid Earth. In another development, this thesis shows how the obtained virtual recordings may be used for migration. With these two contributions, this thesis shows that for elastic surface seismic data, the main drawbacks of migration and interferometry can be overcome using the Marchenko method: multiples do not harm migrated images, and sources (receivers) need not be physically placed in the medium for their responses to be accessible. In addition to the above methods, generating images devoid of multiple-related artifacts can be achieved in several other different ways. Two approaches to this are the use of a post-imaging filter, and attenuation of internal multiples in the data itself. This thesis contributes one new method using each of these approaches. First, a form of Marchenko imaging is known to create spurious reflectors, as also occurs in standard reverse-time migration (RTM). However, these artifacts usually appear at different locations in RTM and this form of Marchenko imaging. Using this insight, this thesis presents a way to combine pairs of seismic images in such a way that their differences (e.g. artifacts) are attenuated, while similarities (e.g. true reflectors) are preserved. Applying this to RTM and Marchenko-derived images markedly improves image quality. Second, this thesis presents a method to estimate multiples in the data. Multiples can either be migrated on their own to aid in interpretation, or be adaptatively removed from the data to improve image quality. However, because of the nature of adaptive subtraction, this second method may harm primary energy. To avoid this problem, this thesis develops a final method to directly image using only primary energy in the recorded data using only a small number of virtual points. This method bypasses the need for multiple removal and the estimation of subsurface responses at every depth location. In addition, primaries from particular reflectors may be particularly selected such that they can be imaged individually. Overall this thesis provides several new ways to use surface seismic data in such a way that multiples do not hamper the end product of seismic data processing: the seismic image. It demonstrates this use on synthetic and real data, proving their effectiveness.