This paper studies physical-layer secure transmissions from a transmitter to a legitimate receiver against an eavesdropper over slow fading channels, taking into account the impact of finite blocklength secrecy coding. A comprehensive analysis and optimization framework is established to investigate secrecy throughput for both single- and multi-antenna transmitter scenarios. Both adaptive and non-adaptive design schemes are devised, in which the secrecy throughput is maximized by exploiting the instantaneous and statistical channel state information of the legitimate receiver, respectively. Specifically, optimal transmission policy, blocklength, and code rates are jointly designed to maximize the secrecy throughput. Additionally, null-space artificial noise is employed to improve the secrecy throughput for the multi-antenna setup with the optimal power allocation derived.Various important insights are developed. In particular, 1) increasing blocklength benefits both reliability and secrecy under the proposed transmission policy; 2) secrecy throughput monotonically increases with blocklength; 3) secrecy throughput initially increases but then decreases as secrecy rate increases, and the optimal secrecy rate maximizing the secrecy throughput should be carefully chosen in order to strike a good balance between rate and decoding correctness. Numerical results are eventually presented to verify theoretical findings.