In this paper it is studied the main statistical properties of the class of log-symmetric distributions, which includes bimodal distributions as special cases, and distributions that have heavier/lighter tails than those of the log-normal distribution. This family includes distributions such as log-normal, log-Student-t, harmonic law, Birnbaum- Saunders, Birnbaum-Saunders-t and generalized Birnbaum-Saunders. We derive quantile-based measures of location, dispersion, skewness, relative dispersion and kurtosis for the log-symmetric class, which are appropriate in the context of asymmetric and heavy-tailed distributions. Also, we discuss the parameter estimation under classical and Bayesian approaches. The usefulness of the log-symmetric class is illustrated through the statistical analysis of a real dataset, in which it is compared its performance with that of some competitive and very flexible distributions.