Abstract—Quantum error correction is essential for reliable fault-tolerant quantum computing, necessitating the encoding of information redundantly into physical degrees of freedom to safeguard it against noise. A prominent approach involves continuous variable quantum informationprocessing using bosonic modes [3], [5], [6], [13], [17], [23]. This technique encodes information within the harmonic oscillator’s occupation number space, expressed throughnumber states {|n⟩}∞n=0 [19], position and momentum eigenstates {|x⟩}x∈R and {|p⟩}p∈R [12], or a selection of coherent states {|α⟩}α∈S (for a finite set S) [9]. The initial continuous variable scheme involving bosonic modes is the two-mode "dual-rail" encoding, introduced in1995 [8]. Presently, numerous bosonic codes are under assessment for their potential in fault-tolerant quantum computation. This review will focus on key contenders: firstly, establishing a pragmatic bosonic error model; proceedingto explore three prominent single-mode codes renowned for their robust protection against this model; evaluating the performance of these codes, considering relevant theoreticalaspects based on the work by [2]; and finally, delving into hardware-efficient multi-mode extensions, notable for their strides towards feasible physical implementation. Theseextensions will be situated within the evolving realm of bosonic quantum error correcting codes.