In recent years, speech emotion recognition (SER) has attracted a lot of attention and has many applications in the production of emotional search engines and medical systems. These systems recognize the emotion of a speech signal based on its features and different classification methods. One of the challenges of SER systems is related to the feature extraction stage. Because the emotional features, in different people, depend on their behavior and even personality. This causes the same emotional speech expressed by different speakers to show different emotional features or even different emotions to have similar features. One of another important challenges facing classifiers is the high dimensions of emotional features that make complexity and high computational for them. In this speech, fast classifiers (advances and challenges) like hierarchical extreme learning machine and echo state network will be introduced for SER.