In this article we describe the basic principles of Rydberg atom-based RF sensing and present the development of atomic pulsed RF detection and RF phase sensing establishing capabilities pertinent to applications in communications and sensing. To date advances in Rydberg atom-based RF field sensors have been rooted in a method in which the fundamental physical quantity being detected and measured is the electric field amplitude, $E$, of the incident RF electromagnetic wave. The first part of this paper is focused on using atom-based $E$-field measurement for RF field-sensing and communications applications. With established phase-sensitive technologies, such as synthetic aperture radar (SAR) as well as emerging trends in phased-array antennas in 5G, a method is desired that allows robust, optical retrieval of the RF phase using an enhanced atom-based field sensor. In the second part of this paper we describe our fundamentally new atomic RF sensor and measurement method for the phase of the RF electromagnetic wave that affords all the performance advantages exhibited by the atomic sensor. The presented phase-sensitive RF field detection capability opens atomic RF sensor technology to a wide array of application areas including phase-modulated signal communication systems, radar, and field amplitude and phase mapping for near-field/far-field antenna characterizations.