An accurate internal representation of our current motion and orientation in space is critical to navigate in the world and execute appropriate action. The force of gravity provides an allocentric frame of reference that defines one's motion relative to inertial (i.e., world-centered) space. However, movement in this environment also introduces particular motion detection problems as our internal linear accelerometers, the otolith organs, respond identically to either translational motion or changes in head orientation relative to gravity. According to physical principles, there exists an ideal solution to the problem of distinguishing between the two as long as the brain also has access to accurate internal estimates of angular velocity. Here, we illustrate how a nonlinear integrative neural network that receives sensory signals from the vestibular organs could be used to implement the required computations for inertial motion detection. The model predicts several distinct cell populations that are comparable with experimentally identified cell types and accounts for a number of previously unexplained characteristics of their responses. A key model prediction is the existence of cell populations that transform head-referenced rotational signals from the semicircular canals into spatially referenced estimates of head reorientation relative to gravity. This chapter provides an overview of how addressing the problem of inertial motion estimation from a computational standpoint has contributed to identifying the actual neuronal populations responsible for solving the tilt-translation ambiguity and has facilitated the interpretation of neural response properties.