Ambient backscatter communication enables lowcost low-rate wireless interconnections for Internet of Things (IoT) applications. In this work, new signal detectors for different cases of ambient backscatter communications are derived. Specifically, both coherent and partially coherent detectors are obtained for Gaussian ambient signals and phase shift keying (PSK) ambient signals. Maximum likelihood detection method and improved energy detection method (including energy detection and magnitude detection as special cases) are adopted. Numerical results show that the energy detection method has the best performance when the ambient signals are Gaussian, while the magnitude detection method has the best performance when the ambient signals are PSK modulated. Both are comparable to the optimum maximum likelihood detection. Numerical results also show that the improved energy detection method is very flexible and that detectors for PSK ambient signals are slightly better than those for Gaussian ambient signals.