We aim to systematically review challenges imposed by emerging distributed energy resources (DERs) to model in two basic distribution management system (DMS) online applications—power flow and short-circuit analysis, as well as to offer a systematic review of potential solutions. In the last decade, electronically coupled DERs became increasingly popular. DERs can employ a wide range of control strategies for power, current, or voltage control, in both normal and faulted conditions. Therefore, DERs cannot be modeled with the traditional PQ (load or generator bus), and PV (generator bus) bus types used for modeling synchronous and induction machines in online power flow calculations. Moreover, because fault currents of DERs are limited to predefined maximal values, electronically coupled DERs cannot be represented with traditional voltage source behind impedance models for online short-circuit calculation (SCC). However, most of the DMS software packages still use the traditional models to represent all DER types, including those that are electronically coupled. This paper shows that there will be high calculation errors in such practice, which makes the system model be an inadequate representation of the system. And this will lead to serious errors in managing, control, and operation of distribution systems. Nonetheless, potential solutions to the challenges are systematically reviewed. Finally, calculation results on a distribution test system with all DER types are used to prove the claim.