Resonance studies have been made on a number of effectively one‐dimensional magnetic systems, elucidating their unique and interesting spin dynamical behavior. These include stacks of planar aromatic organic free radicals, where the most interesting features are associated with temperature dependence. Among these is the crystal NMP‐TCNQ, in which there is evidence for transitions from an antiferromagnetic to paramagnetic insulator to metal as the temperature is raised. A pronounced linewidth peak reflects the large spin fluctuations associated with the establishment of short range order in the (lower) broad transition characteristic of one dimension. More commonly the organic chains are described by a Heisenberg Hamiltonian with very large J:J ∼ .05 − 1 eV, so that J >> kT typically, in contrast to usual studies of paramagnets. This requires modification of the standard high temperature theories of exchange narrowing in paramagnets. We review the detailed evidence for the behavior of the triplet excitons — of either Frenkel or Wannier type — which have been proposed as the dominant paramagnetic excitations in these crystals. Finally we consider two well‐studied inorganic linear chain crystals, CTS (Cu2+ resonance) and TMMC (Mn+ resonance). Explicitly one‐dimensional behavior of the EPR is seen only in the latter, where the predominant effect is the long time persistence (ψ (t) ∼ t−1/2) of spin correlations associated with topological limitations on diffusion in one dimension. Appropriate modification of standard exchange narrowing theory is shown to explain the observed features in detail: a lineshape which is the Fourier transform of exp(‐At3/2) when θ=0 and Lorentzian when θ = 54°, where θ is the angle between the applied field and the chain axis; a linewidth with predominant angular dependence (3 cos2θ − 1)4/3; and the magnitude of the linewidth, intermediate between the unnarrowed value and that expected from standard exchange narrowing theory. Mechanisms which ultimately suppress the t−1/2 diffusive behavior are discussed.