Over the past decade, neural representations have been studied from the lens of low-dimensional subspaces defined by the co-activation of neurons. However, this view has overlooked other forms of covarying structure in neural activity, including i) condition-specific high-dimensional neural sequences, and ii) representations that change over time due to learning or drift. In this talk, I will present a new framework that extends the classic view towards additional types of covariability that are not constrained to a fixed, low-dimensional subspace. In addition, I will present sliceTCA, a new tensor decomposition that captures and demixes these different types of covariability to reveal task-relevant structure in neural activity. Finally, I will close with some thoughts regarding the circuit mechanisms that could generate mixed covariability. Together this work points to a need to consider new possibilities for how neural populations encode sensory, cognitive, and behavioral variables beyond neural subspaces.