Accurate signal-to-noise ratio (SNR) and noise variance estimation are extremely important aspects of receiver design in multiple-input multiple-output (MIMO) systems. Typically, these parameters are estimated using known pilot/training symbols. However, significant improvements may be made by using both the known pilot symbols as well as the unknown data symbols. In this paper, we address SNR and noise variance estimation of MIMO systems for both a data aided (DA) model, a non-data aided (NDA) model, as well as a mixed model that uses known and unknown data symbols. The Cramér-Rao lower bound (CRLB) and modified Cramér-Rao lower bound (MCRLB) for MIMO SNR and MIMO noise variance estimation are determined for digital constellations such as BPSK, QPSK, 8PSK, and 16QAM. Maximum-likelihood estimators are derived in closed form for the DA model. For the NDA model, closed form approximations are derived in addition to iterative expectation-maximization (EM) algorithm based estimators, all of which are demonstrated to perform very close to the CRLB.