In this paper, we consider the torsional motion of a drilling system and propose three algorithms to estimate the friction factors that characterize the interaction between the drill pipe and the wellbore walls (Coulomb source terms). This is essential to design the next generation of stick-slip mitigation controllers, to develop real-time wellbore monitoring tools, and to enable effective toolface control for directional drilling. We propose two model-based algorithms (an adaptive observer and a recursive dynamics framework) and a machine learning-based algorithm to estimate friction parameters, all of them presenting advantages and drawbacks. The performances of our modelbased estimators are finally compared with this data-driven neural network.