Neural recording technologies increasingly enable simultaneous measurement of neural activity from multiple brain areas. To gain insight into distributed neural computations, a commensurate advance in experimental and analytical methods is necessary. We discuss two opportunities towards this end: the manipulation and modeling of neural population dynamics. Neural circuits comprise networks of individual neurons that perform sensory, cognitive, and motor functions. Neuronal biophysics, together with these circuits, give rise to neural population dynamics, which express how the activity of the neural population evolves through time in principled ways. Neural population dynamics provide a framework for understanding neural computation. Prior studies have modeled neural population dynamics to gain insight into computations involved in decision-making, timing, and motor control 1. Here, we present emerging opportunities for new experiments and analyses that use a dynamical systems framework to better understand brain circuits, how they interact, and how they relate to behavior. The simplest model of neural population dynamics is a linear dynamical system (LDS). An LDS (Fig. 1a) is described by a dynamics equation (x(t + 1) = Ax(t) + Bu(t)) and an observation equation (y(t) = Cx(t) + d). Typically, y(t) reflects experimental measurements, such as a vector where each element is the number of action potentials fired by a neuron in a brief time bin (e.g., 10 ms). The vector x(t) is a "neural population state" that captures information in y(t). This neural population state can be thought of as a representation of the dominant activity patterns in the experimental neural recordings. Typically, x(t) is an abstract representation in a lowdimensional subspace (or manifold) found via dimensionality reduction 2 (Fig. 1b, neural state), reflecting that the neural activity is correlated and the dominant patterns can be described by a relatively small number of variables. The neural population state can also represent the activity of each neuron in the original dimensionality of the measured data (e.g., 100D if 100 neurons). The observation equation relates the observed action potentials (y(t)) to the neural population state (x(t)) through an observation matrix (C). The vector, d, is a constant offset (e.g., to model baseline firing). The neural population state moves through neural state space, constituting a neural population trajectory. The dynamics equation expresses how the neural population state (x(t)) progresses through time as a function of a dynamics matrix (A), an input matrix (B) and