In this paper, we review the theoretical and experimental progress in understanding the controversial phase behavior of binary liquids in dense porous media. Experimental observation of metastability and hysteresis in the phase-separation behavior has led to two widely different theoretical interpretations: the random-field Ising picture and the single-pore picture. We argue that the random-field model is inapplicable to binary liquids in low-porosity media such as Vycor, and discuss the available experimental evidence on such systems. Next, we present Monte Carlo studies of phase-separation kinetics of an Ising model in a pore. We find that the domain-growth kinetics slow down dramatically once the domain size becomes comparable to the pore size, as predicted by the single-pore model. In addition, we examine the influence of temperature and interfacial phase transitions on the kinetics, and show that the domain-growth rate slows down as the temperature moves further into the two-phase region. Finally, our results for small pores, only 20 spins across, suggest that macroscopic descriptions are surprisingly successful, even at short length scales.