As of this moment, 50 gravitational wave (GW) detections have been announced, thanks to the observational efforts of the LIGO-Virgo collaboration, working with the Advanced LIGO and the Advanced Virgo interferometers. The detection of signals is complicated by the noise-dominated nature of the data. Conventional approaches in GW detection procedures require either precise knowledge of the GW waveform in the context of matched filtering searches or coincident analysis of data from multiple detectors. Furthermore, the analysis is prone to contamination by instrumental or environmental artifacts called glitches which either mimic astrophysical signals or reduce the overall quality of data. In this paper, we propose an alternative generic method of studying GW data based on detecting anomalies. The anomalies we study are transient signals, different from the slow non-stationary noise of the detector. The anomalies presented in the manuscript are mostly based on the GW emitted by the mergers of binary black hole systems. However, the presented study of anomalies is not limited only to GW alone, but also includes glitches occurring in the real LIGO/Virgo dataset available at the Gravitational Waves Open Science Center. To search for anomalies we employ deep learning algorithms, namely convolutional autoencoders, which are trained on both simulated and real detector data. We demonstrate the capabilities of our deep learning implementation in the reconstruction of injected signals. We study the influence of the GW strength, defined in terms of matched filter signal-to-noise ratio, on the detection of anomalies. Moreover, we present the application of our method for the localization in time of anomalies in the studied time-series data. We validate the results of anomaly searches on real data containing confirmed gravitational wave detections; we thus prove the generalization capabilities of our method, towards detecting GWs unknown to our deep learning models during training.