Column base connections are one of the most critical components in Steel Moment Frames (SMFs) since these connections transfer the loads from the entire superstructure to the concrete foundation. Typically, exposed base plates are preferred for low-and mid-rise buildings, while embedded base connections are the norm for tall buildings. Recent experimental programs have demonstrated that these connections pose high ductility capacities and excellent dissipative properties. Apart from this, data collected by some researchers have indicated that column members in the presence of axial compressive forces may have limited ductility due to the local buckling phenomenon. These issues have motivated researchers to explore alternative weak base-strong column design approaches. For these purposes, uniaxial material models have been proposed to simulate the behavior of base connections and examine their influence on the seismic response of SMFs using Nonlinear Time History Analyses (NTHA). This paper presents two uniaxial material models developed in the OpenSEES platform for exposed and embedded base connections and their application on NTHA. The uniaxial models consist of a backbone curve, with rules that define the connection’s hysteretic behavior and rules that capture their cyclic deterioration characteristics. Analytical methods are used to compute the core parameters (e.g., rotational stiffness, peak strength) of the models, while optimization techniques are employed to estimate ancillary parameters (e.g., deterioration parameters). Results of the NTHA indicate that the base-connection design forces can be reduced safely by incorporating their high deformation capacities as part of the energy dissipative mechanisms. Limitations of the models are discussed, and lines for future research are outlined.