To optimize the processing of spatial queries, there is an increasing interest in combining <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spatial index structures</i> with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">modern storage devices</i> like flash-based Solid State Drives, PCM, and 3D Xpoint. These devices have several advantages compared to classical Hard Disk Drives, such as lower power consumption, and faster reads and writes. However, modern storage devices have changed the paradigm of data management because of their intrinsic characteristics, such as asymmetric read and write costs. Intending to exploit the benefits of modern storage devices, the development of spatial index structures for these devices has been an emerging research topic with recent and constant advances in the literature. This includes the adaptation of existing spatial index structures like the R-tree, or even the design of innovative structures. In this article, we present a comprehensive survey that highlights the key ideas, compares the main characteristics, and discusses the advantages and disadvantages of spatial index structures for modern storage devices. Further, we study how experimental evaluations have been conducted to empirically compare these structures. Finally, we discuss challenges and identify potential future trends when indexing spatial data in this era of modern storage devices.