We study a novel communication mechanism, ambient backscatter, that utilizes radio frequency (RF) signals transmitted from an ambient source as both energy supply and information carrier to enable communications between low-power devices. Different from existing non-coherent schemes, we here design the semi-coherent detection, where channel parameters can be obtained from unknown data symbols and a few pilot symbols. We first derive the optimal detector for the complex Gaussian ambient RF signal from likelihood ratio test and compute the corresponding closed-form bit error rate (BER). To release the requirement for prior knowledge of the ambient RF signal, we next design a suboptimal energy detector with ambient RF signals being either the complex Gaussian or the phase shift keying (PSK). The corresponding detection thresholds, the analytical BER, and the outage probability are also obtained in closed-form. Interestingly, the complex Gaussian source would cause an error floor while the PSK source does not, which brings nontrivial indication of constellation design as opposed to the popular Gaussian-embedded literatures. Simulations are provided to corroborate the theoretical studies.