Intensity- and amplitude-weighted average lifetimes, denoted as tau(I) and tau(A) hereafter, are useful indicators for revealing Forster resonance energy transfer (FRET) or fluorescence quenching behaviors. In this work, we discussed the differences between tau(I) and tau(A) and presented several model-free lifetime determination algorithms (LDA), including the center-of-mass, phasor, and integral equation methods for fast tau(I) and tau(A) estimations. For model-based LDAs, we discussed the model-mismatch problems, and the results suggest that a bi-exponential model can well approximate a signal following a multi-exponential model. Depending on the application requirements, suggestions about the LDAs to be used are given. The instrument responses of the imaging systems were included in the analysis. We explained why only using the tau(I) model for FRET analysis can be misleading; both tau(I) and tau(A) models should be considered. We also proposed using tau(A)/tau(I) as a new indicator on two-photon fluorescence lifetime images, and the results show that tau(A)/tau(I) is an intuitive tool for visualizing multi-exponential decays.