Growing interest in automatic speaker verification (ASV) systems has lead to significant quality improvement of spoofing attacks on them. Many research works confirm that despite the low equal error rate (EER) ASV systems are still vulnerable to spoofing attacks. In this work we overview different acoustic feature spaces and classifiers to determine reliable and robust countermeasures against spoofing attacks. We compared several spoofing detection systems, presented so far, on the development and evaluation datasets of the Automatic Speaker Verification Spoofing and Countermeasures (ASVspoof) Challenge 2015. Experimental results presented in this paper demonstrate that the use of magnitude and phase information combination provides a substantial input into the efficiency of the spoofing detection systems. Also waveletbased features show impressive results in terms of equal error rate. In our overview we compare spoofing performance for systems based on different classifiers. Comparison results demonstrate that the linear SVM classifier outperforms the conventional GMM approach. However, many researchers inspired by the great success of deep neural networks (DNN) approaches in the automatic speech recognition, applied DNN in the spoofing detection task and obtained quite low EER for known and unknown type of spoofing attacks.