The mechanism for the formation of singlet and triplet states in conjugated polymer-based light-emitting diodes (LEDs) is crucial in determining the overall efficiencies of these devices. If simple spin statistics apply then singlets and triplets should be formed in the ratio 25:75. However, the non-emissive nature of triplet states in these materials, as well as other loss mechanisms within the devices, mean that this ratio is not straightforward to measure. Nevertheless, recent experimental advances have made it possible to determine many of the properties of triplet states. Here we review what is now known about triplet states and their photophysics in conjugated polymers. We place particular emphasis on measurements of the singlet generation fraction in LEDs, and discuss the experimental techniques that have been used, such as direct comparison of photoluminescence and electroluminescence efficiencies, triplet absorption cross section measurements and magnetic resonance measurements. All of these techniques give values for the singlet generation fraction in polymers that are significantly larger than the 25% expected, and many of them have also shown that in shorter oligomers this value decreases to be closer to 25%. We also give a brief overview of recent theories for the processes of singlet and triplet formation in polymer devices.