In 1979, an epidemiological study carried out in Denver, Colorado first suggested that very weak alternating magnetic fields arising from electrical lines around houses was associated with an increased risk of cancer in children. The potential impact on public health was high, considering the fact that exposure to power-frequency magnetic fields is omnipresent. All power transmission and distribution networks, domestic and industrial wiring, and all kinds of electrical equipment give off magnetic fields. The hypothesis was taken seriously and substantial research budgets have been devoted not only to answering the important question raised by this study but more broadly to identify all other potential health effects of magnetic fields. Since 1979, an exceptional number of scientific studies have been published worldwide. In 2007, the World Health Organization published one of the most comprehensive review so far. The present article summarizes important facts regarding the interaction between a magnetic field and the human body and the key findings from this extensive research looking for a possible link with cancer.