Electromagnetic observations of the sky have been the basis for our study of the Universe for millennia, cosmic ray studies are now entering their second century, the first neutrinos from an astrophysical source were identified three decades ago, and gravitational waves were directly detected only four years ago. Detections of these messengers are now common. Astrophysics will undergo a revolution in the 2020s as multimessenger detections become routine. The 8th Astro2020 Thematic Area is Multimessenger Astronomy and Astrophysics, which includes the identification of the sources of gravitational waves, astrophysical and cosmogenic neutrinos, cosmic rays, and gamma-rays, and the coordinated multimessenger and multiwavelength follow-ups. Identifying and characterizing multimessenger sources enables science throughout and beyond astrophysics. Success in the multimessenger era requires: (i) sensitive coverage of the non-electromagnetic messengers, (ii) full coverage of the electromagnetic spectrum, with either fast-response observations or broad and deep high-cadence surveys, and (iii) improved collaboration, communication, and notification platforms.