Advancements in satellite technology have made direct-to-device connectivity a viable solution for ensuring global access. This method is designed to provide internet connectivity to remote, rural, or underserved areas where traditional cellular or broadband networks are lacking or insufficient. This paper is a survey providing an in-depth review of multi-satellite Multiple Input Multiple Output (MIMO) systems as a potential solution for addressing the link budget challenge in direct user-satellite communication. Special attention is given to works considering multi-satellite MIMO systems, both with and without satellite collaboration. In this context, collaboration refers to sharing data between satellites to improve the performance of the system. This survey begins by explaining several fundamental aspects of satellite communications (SatComs), which are vital prerequisites before investigating the multi-satellite MIMO systems. These aspects encompass satellite orbits, the structure of satellite systems, SatCom links, including the inter-satellite links (ISL) which facilitate satellite cooperation, satellite frequency bands, satellite antenna design, and satellite channel models, which should be known or estimated for effective data transmission to and from multiple satellites. Furthermore, this survey distinguishes itself by providing more comprehensive insights in comparison to other surveys. It specifically delves into the Orthogonal Time Frequency Space (OTFS) within the channel model section. It goes into detail about ISL noise and channel models, and it extends the ISL section by thoroughly investigating hybrid FSO/RF ISLs. Furthermore, analytical comparisons of simulation results from these works are presented to highlight the advantages of employing multi-satellite MIMO systems.