On large classes of closed even-dimensional Riemannian manifolds M, we construct and study the Copolyharmonic Gaussian Field, i.e. a conformally invariant log-correlated Gaussian field of distributions on M. This random field is defined as the unique centered Gaussian field with covariance kernel given as the resolvent kernel of Graham-Jenne-Mason-Sparling (GJMS) operators of maximal order. The corresponding Gaussian Multiplicative Chaos is a generalization to the 2m-dimensional case of the celebrated Liouville Quantum Gravity measure in dimension two. We study the associated Liouville Brownian motion and random GJMS operator, the higher-dimensional analogues of the 2d Liouville Brownian Motion and of the random Laplacian. Finally, we study the Polyakov-Liouville on the space of distributions on M induced by the copolyharmonic Gaussian field, providing explicit conditions for its finiteness and computing the conformal anomaly. (arXiv:2105.13925, joint work with Ronan Herry, Eva Kopfer, Karl-Theodor Sturm)