Speed, resolution and sensitivity of today's fluorescence bioimaging can be drastically improved by fluorescent nanoparticles (NPs) that are many-fold brighter than organic dyes and fluorescent proteins. While the field is currently dominated by inorganic NPs, notably quantum dots (QDs), fluorescent polymer NPs encapsulating large quantities of dyes (dye-loaded NPs) have emerged recently as an attractive alternative. These new nanomaterials, inspired from the fields of polymeric drug delivery vehicles and advanced fluorophores, can combine superior brightness with biodegradability and low toxicity. Here, we describe the strategies for synthesis of dye-loaded polymer NPs by emulsion polymerization and assembly of pre-formed polymers. Superior brightness requires strong dye loading without aggregation-caused quenching (ACQ). Only recently several strategies of dye design were proposed to overcome ACQ in polymer NPs: aggregation induced emission (AIE), dye modification with bulky side groups and use of bulky hydrophobic counterions. The resulting NPs now surpass the brightness of QDs by ≈10-fold for a comparable size, and have started reaching the level of the brightest conjugated polymer NPs. Other properties, notably photostability, color, blinking, as well as particle size and surface chemistry are also systematically analyzed. Finally, major and emerging applications of dye-loaded NPs for in vitro and in vivo imaging are reviewed.