Described herein are multi-channel noise suppression systems and methods that are configured to detect and suppress wind and background noise using at least two spatially separated microphones: at least one primary speech microphone and at least one noise reference microphone. The multi-channel noise suppression systems and methods are configured, in at least one example, to first detect and suppress wind noise in the input speech signal picked up by the primary speech microphone and, potentially, the input speech signal picked up by the noise reference microphone. Following wind noise detection and suppression, the multi-channel noise suppression systems and methods are configured to perform further noise suppression in two stages: a first linear processing stage that includes a blocking matrix and an adaptive noise canceler, followed by a second non-linear processing stage.