We will start with the formula of Siegel and Weil, which identifies a weighted average of theta series attached to positive definite lattices (over integers) with a certain more explicit generating series, called Eisenstein series. A special case gives Siegel's mass formula expressing the weighted number of such lattices of a given dimension in terms of Bernoulli numbers. For non-definite lattices, there is an "arithmetic" analog of theta series, as a generating series of special topological cycles on certain locally symmetric spaces. When these locally symmetric spaces admit algebraic structure (in our case, they are moduli spaces of abelian varieties or K3 surfaces), the topological cycles are algebraic cycles (defined over rational numbers or integers). The arithmetic intersection numbers (an arithmetic analog of "linking numbers") of these cycles have recently been determined and are shown to be related to the derivative (with respect to a suitable complex parameter) of suitable Eisenstein series. We will finish with mentioning some applications of these results to quetions about algebraic cycles on such moduli spaces and L-functions. No prior knowledge on any of these is required!