The electronic and magnetic properties of different arsenene nanoribbon (As NR) structures were investigated systematically using the density functional theory (DFT) method. Our results reveal that the nanoribbons' geometrical structure and chemical termination have significant impacts on their electronic and magnetic properties. Specifically, the unpassivated armchair nanoribbons (a-NRs) and reconstructed zigzag nanoribbons (zz-o-RNs) are nonmagnetic indirect and direct bandgap semiconductors, respectively. Considering the magnetic interaction between the edge states, the normal and one-atom terminated zigzag nanoribbons (z-NRs) are determined to be a weak antiferromagnetic (AFM) semiconductor. H passivation at the edge sites results in nonmagnetic and semiconducting properties of a-NRs, z-NRs, and zz-o-NRs. External strain has significant effects on both the band gap and the orbital characteristics of the band edge of a-NRs, zz-o-NRs and H passivated z-NRs, owing to the competition between the As px, py, and pz bonding/anti-bonding states. For the bare z-NRs, the tensile strain stabilizes the AFM state with enhanced magnetic moments. These versatile electronic and magnetic properties suggest possible potential of the As NRs for application in nanoelectronic devices.