Basic algorithmic and numerical issues involved in subspace-based linear multivariable discrete-time system identification are described. A new identification toolbox—SLIDENT—has been developed and incorporated in the freely available Subroutine Library in Control Theory (SLICOT). Reliability, efficiency, and ability to solve industrial identification problems received a special consideration. Two algorithmic subspace-based approaches (MOESP and N4SID) and their combination, and both standard and fast techniques for data compression are provided. Structure exploiting algorithms and dedicated linear algebra tools enhance the computational efficiency and reliability. Extensive comparisons with the available computational tools based on subspace techniques show the better efficiency of the SLIDENT toolbox, at comparable numerical accuracy, and its capabilities to solve identification problems with many thousands of samples and hundreds of parameters.