One fundamental paradigm in engineering is to break a structure into simpler components in order to simplify test and analysis. In the numerical world this concept is the basis for Finite Element discretization and is also used in model reduction through substructuring. In experimental dynamics, substructuring approaches are commonly used (for instance for Transfer Path Analysis) , although the subtleties involved are perhaps not always adequately appreciated. Recently there has been renewed interest in using measurements alone to create dynamic models for certain components and then assembling them with numerical models to predict the behavior of an assembly. Substructured models are also highly versatile; when one component is modified it can be readily assembled with the unchanged parts to predict the global dynamical behavior. Substructuring concepts are critical to engineering practice in many disciplines, and they hold the potential to solve pressing problems in testing and modeling structures where nonlinearities cannot be neglected. In this short course we will review a general framework which can be used to describe a multitude of methods and the fundamental concepts underlying substructuring. The course is aimed at explaining the main concepts as well as specific techniques needed to successfully apply substructuring both numerically (i.e. using finite element models) and experimentally. Therefore, hands-on exercises will be included to illustrate the concepts using routines written in Matlab® and real-life applications will be presented. The course is centered around the following topics, which range from classical substructuring methods to topics of current research such as substructuring for nonlinear systems. 1. Primal and dual assembly of structures and applications to parallel computing. 2. Model reduction and substructuring for linear systems including Guyan and Hurty/Craig-Bamtpon reduction, McNeal, Rubin, Craig-Chang, etc... Recently developed interface reduction methods will also be reviewed. 3. Experimental-Analytical substructuring including modal substructuring methods such as the transmission simulator method and frequency domain methods such as impedance coupling. 4. Model reduction and substructuring methods for non-linear systems: Overview of traditional nonlinear FEA including geometric nonlinearity. Nonlinear Normal Modes and other analytical techniques for nonlinear systems will be reviewed to demystify nonlinearity and its effect on structural response. The special case of weakly nonlinear systems will also be treated including experimental identification methods and experimental substructuring. The course is designed to provide practicing engineers or researchers such as PhD students with a firm grasp of the fundamentals as well as a thorough review of current research in emerging areas. Attendees are expected to have a solid foundation in structural dynamics and some exposure to finite element analysis. The course material will be of interest to those who primarily perform finite element simulations of dynamic structures, to those who primarily focus on modal test, and to those who work at the interface between test and analysis.