In the last two decades thousands of exoplanets have been discovered, showing that planets are ubiquitous throughout the Milky Way. However, the formation of planets itself remains a mystery. Protoplanetary disks of gas and dust around young stars are the birth cradles of planets, and analyzing their properties and structures give further insight in the planet formation process. The Atacama Large Millimeter/submillimeter Array (ALMA) allows us to take very detailed observations of the cold material in protoplanetary disks through submillimeter observations of the thermal dust continuum and rotational molecular lines. Using interferometry, it is now possible to zoom in into these disks down to the scales of distances in our Solar System, while these disks are 100-200 parsec away. ALMA has revolutionized our view of protoplanetary disks: rather than smooth profiles, it has turned out that disks contain gaps, rings, asymmetries and spiral arms, all indicators of active disk dynamics and recently formed planets. The observations are of such exquisite detail that they can be compared directly with predictions of hydrodynamical models of disk evolution and planet-disk interaction. Due to its high sensitivity, ALMA also allows us to do large surveys of hundreds of disks, and statistical studies can now be compared with exoplanet studies. I will show an overview of ALMA discoveries in the last few years and discuss the implications for our understanding of planet formation.