Polycrystalline (PC) and single crystalline (SC) Ca-doped LaCoO3 (LCCO) samples with the perovskite structure were synthesized by conventional solid-state reaction and the floating-zone growth method. We present the results of a comprehensive investigation of the magnetic properties of the LCCO system. Systematic measurements have been conducted on dc magnetization, ac susceptibility, exchange-bias, and the magnetocaloric effect. These findings suggest that complex structural phases, ferromagnetic (FM), and spin-glass/cluster-spin-glass (CSG), and their transitions exist in PC samples, while there is a much simpler magnetic phase in SC samples. It was also of interest to discover that the CSG induced a magnetic field memory effect and an exchange-bias-like effect, and that a large inverse irreversible magnetocaloric effect exists in this system.