In IoT healthcare platform, a variety of biosignals are acquired from its sensors and appropriate feature extraction techniques are crucial in order to make use of the acquired biosignal data and help the healthcare scientist or bio-engineer to reach at optimal decisions. This work reviews the existing biosignal feature extraction and classification methods for different healthcare applications. Due the enormous amount of different biosignals and since most healthcare applications uses electrocardiogram (ECG), electroencephalogram (EEG), electromyogram (EMG), Electrogastrogram (EGG), we focus the review on feature extractions and classification method for these biosignals. The review also includes a summary of Blood Oxygen Saturation determined by Pulse Oximetry (SpO2), Electrooculography and eye movement (EOG), and Respiration (RSP) signals. Its discussion and analysis focuses on advantages, performance and drawbacks of the techniques.