In this article, we present two clustered sparse Bayesian learning (Cluster-SBL) channel estimation algorithms for millimeter-wave (mmWave) massive multiple-input-multiple-output (MIMO) systems. Different from prior literature, channel path correlations at both the transmitter and the receiver are considered and exploited for estimation performance enhancement. Specifically, we first propose a Kronecker product-based multivariate Gaussian (KP-Gaussian) prior model for mmWave massive MIMO channels, which captures not only sparsity but also the widely existing clustering channel property in mmWave communications. Then, a channel approximation method is derived and leveraged to overcome the challenge caused by channel priors' uncertainty due to the varying propagation environments and improve the robustness of the channel estimation algorithm against channel sparsity. After that, the Cluster-SBL channel estimation algorithm, which is developed based on the expectation maximization (EM) framework and has superior estimation accuracy and high robustness, is proposed. Moreover, to reduce the computation complexity in the channel estimation for practical applications, we also propose an efficient Cluster-SBL (eCluster-SBL) channel estimation algorithm. It is highly beneficial to mmWave massive MIMO systems, especially when the angular resolution is relatively high. Numerical results reveal that, compared with the existing compressed sensing-based and Bayesian criterion-based algorithms, the proposed two channel estimation algorithms exhibit the better performance from both the aspect of estimation accuracy and the aspect of robustness.