Analytical and experimental methods are provided for estimating synaptic connectivities from simultaneous recordings of multiple neurons. The results are based on detailed, yet flexible neuron models in which spike trains are modeled as general doubly stochastic point processes. The expressions derived can be used with non-stationary or stationary records, and can be readily extended from pair-wise to multi-neuron estimates. Furthermore, we show analytically how the estimates are improved as more neurons are sampled, and derive the appropriate normalizations to eliminate stimulus-related correlations. Finally, we illustrate the use and interpretation of the analytical expressions on simulated spike trains and neural networks, and give explicit confidence measures on the estimates.