Self-assembled linear structures like giant cylindrical micelles or discotic molecules in solution stacked in flexible columns are systems reminiscent of polydisperse polymer solutions, ranging from dilute to concentrated solutions as the overall monomer density and/or the chain length increases. These supramolecular polymers have an equilibrium length distribution, the result of a competition between the random breakage of chains and the fusion of chains to generate longer ones. This scissionrecombination mechanism is believed to be responsible of some peculiar dynamical properties like the Maxwell fluid rheological character for entangled micelles. Simulations employing simple mesoscopic models provide a powerful approach to test mean-field theories or scaling approaches which have been proposed to rationalize the structural and kinetic properties of these soft matter systems. In the present work, we review the basic theoretical concepts of these "equilibrium polymers" and some of the important results obtained by simulation approaches. We propose a new version of a mesoscopic model in continuous space based on the bead and FENE spring polymer model which is treated by Brownian Dynamics and Monte-Carlo binding/unbinding reversible changes for adjacent monomers in space, characterized by an attempt frequency parameter ω. For a dilute and a moderately semi-dilute state-points which both correspond to dynamically unentangled regimes, the dynamic properties are found to depend upon ω through the effective life time τ b of the average size chain which, in turn, yields the kinetic reaction coefficients of the mean-field kinetic model proposed by Cates. Simple kinetic theories seem to work for times t ≥ τ b while at shorter time, strong dynamical correlation effects are observed. Other dynamical properties like the overall monomer diffusion and the mobility of reactive end-monomers are also investigated.