Accreting compact objects are among the most variable sources in the X-ray sky. In X-ray binaries, the conversion of gravitational energy into radiation provides a powerful laboratory for studying accretion under extreme conditions, while variability on timescales ranging from milliseconds to years offers a unique probe of physical processes occurring close to neutron stars and black holes.

In this talk, I will discuss how X-ray timing and spectroscopy can investigate the physics and geometry of accretion flows, with particular emphasis on neutron-star low-mass X-ray binaries and accreting millisecond X-ray pulsars. Their rapid variability and coherent pulsations provide a direct view of the interaction between the accretion flow, the magnetic field, and the rapidly rotating neutron-star surface, while their transient behaviour allows us to follow how these processes evolve as the accretion rate changes.

I will then broaden the discussion to the emerging opportunities offered by time-domain X-ray astronomy. Wide-field monitoring and rapid follow-up are changing how we discover and study transient and variable sources, providing access to accretion phases that pointed observations alone can easily miss. 

I will briefly discuss the HERMES concept and its pathfinder experience as an example of distributed high-energy monitoring, and then highlight the new discovery space opened by facilities such as Einstein Probe and their synergy with sensitive pointed X-ray observatories.

I will conclude with a perspective on how combining wide-field discovery, rapid multi-wavelength follow-up, and high-sensitivity timing and spectroscopy can help us build a more complete picture of accretion onto compact objects and explore the variable X-ray sky in the coming years.