In this paper, we propose time-based localization approaches for asynchronous wireless sensor networks (WSNs), where not only clock skews but also clock offsets are present at all nodes. We first propose a joint synchronization and localization approach using the two-way ranging (TWR) protocol. Furthermore, a novel ranging protocol, namely asymmetric trip ranging (ATR), is employed and a two-step joint synchronization and localization approach is developed. As a result, we achieve efficient closed-form least-squares (LS) estimators. We compare these two proposed approaches. Moreover, simulation results corroborate the efficiency of our time-based localization schemes.