Since the dawn of Big Data, the exponentially increasing demands for larger data volumes and higher information processing speeds have given the field of spintronics an astonishing momentum. In spintronics, the electron spins and their associated magnetic moments interplay with electronic charges, lattices, and even photons. These diverse interactions open endless possibilities for a new generation of fast, efficient, and non-volatile memory and logic devices to serve and fuel Big Data. Lying at the heart of innovating spintronic memory and logic devices is the search for advanced materials and mechanisms to control spin and magnetism.Following this line of research, this dissertation focuses on exploring two emerging material classes, namely, topological insulators and ferrimagnets, which hold great promise for efficient and fast magnetization manipulation. More specifically, topological insulators exhibit an extraordinary charge-spin conversion efficiency owing to their exotic surface states and can be employed to manipulate magnetic moments with minimal energy. Ferrimagnets, by contrast, are of technical interest for fast magnetization manipulation because their two non-equivalent and antiparallel aligned sublattices uniquely combine the antiferromagnet-like ultrafast dynamics with the ferromagnet-like readability/controllability for well-established techniques. However, these novel materials have been difficult to investigate using conventional magnetometers or magnetic resonance techniques. To address these challenges, an experimental platform integrating a magneto-optical Kerr effect magnetometer, a femtosecond optical pump-probe technique, and common magneto-transport measurements, was first established. Using this experimental platform, the charge-spin conversion efficiency was investigated and accurately quantified for a topological insulator-based magnetic bilayer, and a critical role of the topological surface states with spin-momentum locking was unveiled. With innovative material engineering, topological insulators were integrated with widely used metallic ferromagnet in a topological insulator/Mo/CoFeB/MgO structure. This topological insulator/Mo/CoFeB/MgO structure demonstrates high thermal stability, robust magnetic properties, and efficient magnetization switching driven by spin-orbit torques. The systematically calibrated efficiency confirms that, for a room temperature magnetic memory, topological insulators are at least one order of magnitude more efficient than conventional heavy metals. Moreover, the annealing effects were carefully studied in this structure, and desirable thermal compatibility with modern CMOS technology has also been achieved, empowering the development of advanced spintronic applications. To realize faster control of magnetic moments, the dynamical characteristics of a compensated ferrimagnetic GdFeCo film with a vertical compositional gradient were investigated through the laser-induced ultrafast spin dynamics. It is found that the vertical composition gradient significantly alters the ultrafast spin dynamics. Surprisingly, these distinct spin dynamics can be handily controlled by tuning the power of laser excitation, indicating the existence of more efficient energy pathways to control magnetization with high speed. These observations motivate ferrimagnets with a composition gradient as an ideal candidate for efficient and fast magnetization manipulation. Emboldened by the findings in this dissertation, topological insulators and ferrimagnets undoubtedly possess a vast potential in increasing the efficiency and speed of magnetization manipulation for advancing spintronic memory and logic devices.