Improving the functioning and the safety of the electrical grids is a topic of great concern, given its magnitude and importance in today's world. In this thesis, we focus in these two subjects. In the first part, we study undetectable cyber-physical attacks on power grids, which are attacks that involve physical disruptions, including tripping lines and load modifications, and sensor output alterations. We propose a sophisticated attack model described under the full Alternating Current (AC) power flow equations and show its feasibility on large grids from a test cases library. As counter-measures, we propose different defensive strategies that the network's controller can apply under a suspected cyber attack. These are random, simple and fast procedures that change the voltages across the network and aim to unmask the current status of the system, assuming that the attacker cannot react against their randomness. Secondly, with access to data collected through Phasor Measurement Units (PMUs) by a power utility in the United States, we perform statistical analyses on the frequency and voltage time series that have been recorded at a rate of 30 Hz. We focus on intervals of time where the sampled data shows to be in steady-state conditions and, with the use of appropriate signal processing filters, we are able to extract hidden anomalies such as spatio-temporal correlations between sensors and harmonic distortions.