In this work, first the Cramer-Rao lower bound (CRLB) of the signal-to-noise ratio (SNR) estimate for binary phase shift keying (BPSK) modulated signals in additive white Gaussian noise (AWGN) channels is derived. All the steps and results of this CRLB derivation are shown in a detailed manner. Two major estimation scenarios are considered herein: the non-data-aided (NDA) and data-aided (DA) frameworks, respectively. The non-data-aided scenario does not assume the periodic transmission of known data symbols (pilots) to limit the system throughput, while the data-aided scenario assumes the transmission of known transmit data symbols or training sequences to estimate the channel parameters. The Cramer-Rao lower bounds for the non-data-aided and data-aided scenarios are derived. In addition, the modified Cramer-Rao lower bound (MCRLB) is also calculated and compared to the true CRLBs. It is shown that in the low SNR regime the true CRLB is tighter than the MCRLB in the non-data-aided estimation scenario. Second, the Bayesian Cramer-Rao lower bound (BCRLB) for SNR estimate is considered for BPSK modulated signals in the presence of time-selective fading channels. Only the data-aided scenario is considered, and the time-selective fading channel is modeled by means of a polynomial function. A BCRLB on the variance of the SNR estimate is found and the simulation results are presented.