Large-scale multidisciplinary design optimization (MDO) is the application of numerical optimization to engineering design problems involving hundreds of design variables and complex, multidisciplinary models. Large-scale MDO relies on multidisciplinary adjoint sensitivity analysis methods, which enable the computation of objective gradients and constraint Jacobians at a cost independent of the number of design variables. In the past decade, multiple software frameworks and modeling languages have emerged as options for enabling this critical task of computing derivatives of heterogeneous and multidisciplinary computational models. This talk will review the recent advances that have made large-scale MDO feasible and have automated much of the implementation effort required for multidisciplinary adjoint sensitivity analysis. In particular, we will discuss an emerging graph-based modeling paradigm that automates adjoint sensitivity analysis for a large class of computational models. In this paradigm, the engineer implements the computational model in a domain-specific programming language that enables the construction of a low-level computational graph that, in turn, enables the application of adjoint-based algorithmic differentiation methods. We will also discuss secondary benefits of this graph-based modeling paradigm, such as automatic parallelization of models and acceleration of uncertainty propagation algorithms. We will then discuss an open- source aircraft design optimization framework that has been recently developed within this graph-based modeling paradigm, providing a unique large-scale MDO capability. Finally, the talk will present specific demonstrations of large-scale MDO to urban air mobility vehicle design problems that represent major steps toward industrial-complexity MDO, i.e., MDO with large numbers of disciplines, design variables, constraints, and operating conditions considered.