Ground-based telescopes observing at millimeter (mm) and submillimeter (submm) wavelengths have to deal with a line-rich and highly variable atmospheric spectrum, both in space and time. Models of this spectrum play an important role in planning observations that are appropriate for the weather conditions and also calibrating those observations. Through magnetic dipolar (M1) rotational transitions and electric dipolar (E1) transitions O 2 and H 2 O, respectively, dominate the atmospheric opacity in this part of the electromagnetic spectrum. Although O 2 lines, and more generally the so-called dry opacity, are relatively constant, the absorption related to H 2 O can change by several orders of magnitude leading from a totally opaque atmosphere near sea level with high H 2 O columns to frequency windows with good transmission from high and dry mountain sites. Other minor atmospheric gases, such as O 3 and N 2 O among others, are present in the atmospheric spectrum which also includes nonresonant collision-induced absorption due to several mechanisms. The aim of our research is to improve the characterization of the mm/submm atmospheric spectrum using very stable heterodyne receivers with excellent sideband separation and extremely high (kHz) spectral resolutions at the 5000 m altitude Chajnantor site in northern Chile. This last aspect (spectral resolution) is the main improvement (by more than three orders of magnitude) in the presented data with respect to our previous work conducted ∼20 yr ago from Mauna Kea in Hawai'i. These new measurements have enabled us to identify slight modifications needed in the Atmospheric Transmission at Microwaves (ATM) model to better take into account minor constituent vertical profiles, include a few missing lines, and adjust some high-energy O 3 line frequencies. After these updates, the ATM model is highly consistent with all data sets presented in this work (within ∼2% at 1 GHz resolution).