In a piezoelectric energy harvesting (PEH) system, the dynamics of the device as well as the energy flow within the system vary with different harvesting interface circuits connected. Meanwhile, the impedance matching theory is regarded as theoretical base for harvesting power enhancement, and hopefully could provide guidance for harvesting interface optimization. Most previous literatures on impedance matching for PEH started their analyses by assuming that the harvesting interface, which is nonlinear in nature, can be equalized to resistive load, or linear load whose impedance value can be arbitrarily set, so that the output impedance of the piezoelectric structure can surely be matched. Yet, after investigating the equivalent impedances of the existing harvesting interfaces, including standard energy harvesting (SEH), parallel synchronized switching harvesting on inductor (P-SSHI), and series synchronized switching harvesting on inductor (S-SSHI), we found that, their ranges are in fact limited. Therefore, to optimize the harvesting power, constrained matching instead of free matching should be adopted. In addition, we also clarify some confusing points in the previous literatures on impedance matching for energy harvesting. With the understanding on energy flow within piezoelectric devices, we know that only a portion of the extracted energy is able to be harvested, while the other is dissipated throughout the harvesting process. So even the extracted power from the source is maximized by matching the impedance; there is no guarantee that harvesting power is surely improved. The harvesting power also depends on the ratio between harvested energy and dissipated energy. These two issues discussed in this paper are crucial to improve the harvesting power and efficiency in piezoelectric energy harvesting systems.