Title: Formation and Evolution of Accreting Compact Objects

Abstract: Accreting compact objects are crucial to understand several important astrophysical phenomena such as Type Ia supernovae, gravitational waves, or X-ray and $\gamma$-ray bursts. In addition, they are natural laboratories to infer fundamental properties of stars, to investigate high-energy phenomena and accretion processes, to test theories of stellar and binary evolution, to explore interactions between high-density plasma and very strong magnetic fields, to examine the interplay between binary evolution and dynamical interactions (in the case they belong to dense star clusters), and they can even be used as a probe for the assembling process of galaxies over cosmic time-scales. Despite the fundamental importance of accreting compact objects for astrophysics and recent progress with the comprehension of these fascinating objects, we still do not fully understand how they form and evolve. In this chapter, we will review the current theoretical status of our knowledge on these objects, and will discuss standing problems and potential solutions to them.