<p>The GNSS State Space Representation (SSR) technology is widely accepted to be the most versatile approach for real-time GNSS corrections. It is employed in several commercial and scientific PPP and PPP-RTK services. Its main advantage over observation space representation (OSR) techniques (e.g., RTK or network RTK) is the intrinsic support for broadcast applications disseminating corrections to an unlimited number of users.<br />A complete set of SSR corrections consists of the five basic components: clock, orbit, bias, ionosphere, and troposphere corrections for the different GNSS, frequencies, and signals. In a classical OSR service, the lump-sum of these five basic components is computed by the service provider for the user position and sent to the user. This implies that a user does not need to know the underlying models used by the server. In contrast to OSR, an SSR user must compute the influences of the five SSR components itself. For that reason, SSR models are part of an SSR format documentation. The models chosen in different SSR formats are a compromise between target accuracy, complexity, required bandwidth, and computational workload of the rover.<br />In this conference contribution, we give an overview of different ionosphere and troposphere models used in different open SSR formats. The focus is on SSR formats supporting the high resolution atmospheric corrections (Compact SSR, SPARTN, SSRZ, 3GPP-LPP), but also formats with reduced message sets are addressed (IGS-SSR, RTCM-SSR). We motivate the frequently used multi-stage approach to separate atmospheric corrections into functional (spherical harmonics, polynomials) and residual parts. For the ionosphere, we compare different types of polynomials, vertical and slant TEC, and interpolation heights as well as the advantage of a sun-fixed coordinate frame. For the troposphere, we discuss the advantages and disadvantages of metric vs. relative and slant vs. zenith delay corrections, respectively, and This overview of different ionosphere and troposphere models in SSR formats is intended to help an SSR user to choose a suitable SSR service.</p>