In this paper, we propose to utilize intelligent reflecting surfaces (IRSs) for enhancing the physical layer security of wireless communications systems. In particular, an IRS-assisted secure wireless system is considered, where a multi-antenna transmitter communicates with a single-antenna receiver in the presence of an eavesdropper. To maximize the secrecy rate, both the beamformer at the transmitter and the IRS phase shifts are jointly optimized. Based on the block coordinate descent (BCD) and minorization maximization (MM) techniques, two efficient algorithms are developed to solve the resulting non-convex optimization problem for small- and large-scale IRSs, respectively. Simulation results show that IRSs can significantly improve physical layer security if the proposed algorithms are employed. Furthermore, we reveal that deploying large-scale IRSs is more efficient than enlarging the antenna array size of the transmitter for both boosting the secrecy rate and enhancing the energy efficiency.