Voice biometric systems based on automatic speaker verification (ASV) are exposed to spoofing attacks which may compromise their security. To increase the robustness against such attacks, anti-spoofing systems have been proposed for the detection of replay, synthesis and voice conversion based attacks. This paper summarizes the work carried out for the first author’s PhD Thesis, which focused on the development of robust biometric systems which are able to detect zero-effort, spoofing and adversarial attacks. First, we propose a gated recurrent convolutional neural network (GRCNN) for detecting both logical and physical access spoofing attacks. Second, we propose a new loss function for training neural networks classifiers based on a probabilistic framework known as kernel density estimation (KDE). Third, we propose a top-performing integration of ASV and anti-spoofing systems with a new loss function which tries to optimize the whole voice biometric system on an expected range of operating points. Finally, we propose a generative adversarial network (GAN) for generating adversarial spoofing attacks in order to use them as a defense for building higher robust voice biometric systems. Experimental results show that the proposed techniques outperform many other state-of-the-art systems trained and evaluated in the same conditions with standard public datasets.