This paper initially presents the channel modeling for full duplex (FDX) modulating retro-reflector (MRR) freespace optical (FSO) systems under weak-to-strong turbulence conditions. The uplink channel in the MRR FSO communication is a conventional FSO channel that is typically modeled by a Gamma-Gamma (ΓΓ) distribution. The downlink channel is jointly affected by the turbulence-induced fading in two opposite passes as well as the reflection effect of the MRR, and its normalized channel fading can be described as the product of two correlated ΓΓ random variables (RVs). The channel model of the downlink is approximated by a single α-μ distribution via moment matching method. Then, we propose an effective signal modulation and detection scheme to achieve the FDX communication. The bit error rates of the MRR FSO systems are calculated by the analytical formulas that are derived based on the channel models of the two links, and also evaluated by the Monte-Carlo simulations to validate the derived formulas. The effect of system configurations and propagation conditions on the system performance is investigated, and the optimal designs to make a trade-off between the uplink and downlink performance are discussed.