Shortly after the discovery in 1994 of superconductivity in Sr(2)RuO(4), it was proposed on theoretical grounds that the superconducting state may have chiral p-wave symmetry analogous to the A phase of superfluid (3)He. Substantial experimental evidence has since accumulated in favor of this pairing symmetry, including several interesting recent results related to broken time-reversal symmetry (BTRS) and vortices with half of the usual superconducting flux quantum. Great interest surrounds the possibility of chiral p-wave order in Sr(2)RuO(4), since this state may exhibit topological order analogous to that of a quantum Hall state, and can support such exotic physics as Majorana fermions and non-Abelian winding statistics, which have been proposed as one route to a quantum computer. However, serious discrepancies remain in trying to connect the experimental results to theoretical predictions for chiral p-wave order. In this paper, I review a broad range of experiments on Sr(2)RuO(4) that are sensitive to p-wave pairing, triplet superconductivity and time-reversal symmetry breaking and compare these experiments to each other and to theoretical predictions. In this context, the evidence for triplet pairing is strong, although some puzzles remain. The 'smoking gun' experimental results for chiral p-wave order, those which directly look for evidence of BTRS in the superconducting state of Sr(2)RuO(4), are most perplexing when the results are compared with each other and to theoretical predictions. Consequently, the case for chiral p-wave superconductivity in Sr(2)RuO(4) remains unresolved, suggesting the need to consider either significant modifications to the standard chiral p-wave models or possible alternative pairing symmetries. Recent ideas along these lines are discussed.