Microgrids, are small foot-print power systems that balance critical loads against available energy supply, and are capable of operating in both grid-connected and islanded operation modes. Numerous factors such as energy assurance, reliability, renewable integration and economics are driving increased research and development in the modeling, analysis and control of microgrids.In intentionally islanded operation, well-established droop control techniques are employed to keep inverters synchronized and regulate frequency and voltage within stability limits in microgrids. Computationally efficient and accurate models that describe droop-controlled inverter dynamics are key to controller design, stability assessment, and performance evaluation of islanded microgrids. Typical models for droop-controlled inverters are very detailed, and include myriad states from internal control loops and filters. Conceivably, control design, numerical simulations, and stability assessment with such models in islanded microgrids comprising tens of or even hundreds of inverters is computationally expensive and do not offer any analytical insights. This calls for the development of reduced-order models of inverter-based microgrids. Model reduction methods can isolate relevant spatio-temporal dynamics and mutual interactions of interest. While model reduction methods have been widely applied in bulk power systems, a systematic model-reduction procedure for droop-controlled islanded inverters has thus far been lacking. The objective of this thesis is to reduce large-signal dynamic models of inverter-based islanded microgrids in both spatial and temporal aspects. Singular perturbation methods are applied for temporal model reduction, and Kron reduction is employed for the spatial model reduction. The ensuing reduced-order models accurately describe the original dynamics with reduced computational burden. In addition, spatial model reduction isolates the mutual inverter interactions and clearly illustrates the equivalent loads that the inverters have to support in the microgrid - this aspect is leveraged in controller design to minimize power losses and voltage deviations.