Data structures are fundamental to machine learning (ML) systems of today in terms of their performance and scalability. With the increasing exponentially growing datasets in size, dimension, and complexity, traditional data structures, like arrays, linked lists, and trees, cannot provide the responsiveness and flexibility required by the intelligent applications of the present day. The paper is a systematic review of the latest data structures that are optimized to support machine learning processes, their storage, indexing, search, and machine learning computations. It examines the transition of classical data models to tensor-based, graph-based, and distributed models that permit the high-performance learning in various fields. We categorize the modern data structures as they relate to their computational properties, memory consumption, and incorporation as a part of the deep learning platforms. Moreover, according to the survey, key design issues are the sparsity of data, real-time flexibility, and optimization of hardware. Lastly, we describe the new trends which include quantum-inspired and neuromorphic data representations that characterize the next frontier of intelligent computing. The purpose of this review is to act as a resource for researchers and practitioners who want to find effective data organization solutions that will help them speed up machine learning pipelines.