The Atacama Large Millimeter-Submillimeter Array (ALMA) has opened a new window for studying the Sun via high-resolution high-sensitivity imaging at millimeter wavelengths. In this contribution I review the capabilities of the instrument for solar observing and describe the extensive effort taken to bring the possibility of solar observing with ALMA to the scientific community. The first solar ALMA observations were carried out during 2014 and 2015 in two ALMA bands, Band 3 (λ=3 mm) and Band 6 (λ=1.3 mm), in single-dish and interferometric modes, using single pointing and mosaicing observing techniques, with spatial resolution up to ∼2″ and ∼1″ in the two bands, respectively. I overview several recently published studies which made use of the first solar ALMA observations, describe current status of solar observing with ALMA and briefly discuss the future capabilities of the instrument.