X-ray pulsars, powered by accretion onto highly magnetized, rapidly rotating neutron stars, provide a unique laboratory to study extreme physics. Apart from the coherent modulations due to stellar rotation, these systems also exhibit quasi-periodic oscillations (QPOs) and aperiodic variability. In this talk, I will present the results of detailed spectral and timing studies of both transient and persistent X-ray pulsars, focusing on QPOs and their energy- and luminosity-dependent properties.  The sources RX J0440.9+4431, LMC X-4, and 4U 1626-67 serve as excellent examples for exploring these phenomena. In addition, X-ray pulsars and eclipsing binaries offer valuable opportunities to study the precise orbital evolution of binary systems. I will discuss results from two fascinating eclipsing systems: the low-mass X-ray binary (LMXB) XTE J1710-281, which shows intriguing orbital glitches, and the high-mass X-ray binary (HMXB) LMC X-4, where the second derivative of the orbital period reveals its long-term dynamics. I will also highlight key findings from spectral and timing studies of several transient sources during their X-ray outbursts and a few timing results from POLIX and XSPECT data. These results provide new insights into the accretion physics, variability mechanisms, and orbital evolution of X-ray pulsars.