["Journal of Applied Econometrics, EarlyView. ", "\nABSTRACT\nDespite its conceptual appeal, the autoregressive inverse‐Wishart (AIW) multivariate stochastic volatility model has been hindered by inefficient sampling methods. The existing samplers for the latent covariance matrix severely suffer from the curse of dimensionality and only work when the dimension is very low. In this paper, we introduce a new proposal for the latent covariance matrix in the AIW model, which demonstrates far better scalability. We introduce different extensions to the basic AIW model that capture various stylized volatility features. We further fit the AIW model into a factor structure and provide an a posteriori identification procedure without introducing order dependence. When evaluated using real datasets ranging from 10 assets to 1000 assets, the new AIW‐based models, whether the standalone versions or the factor versions, are especially suited for multivariate volatility modeling in a wide range of dimensions.\n"]