Bollux and Blue Max were two droids who, although working irrespective of each other, were symbiotically linked. They were each programmed to feel emotions, and they felt many in the service of Han and Chewie. The two droids were completely different in most respects. Bollux was a century-old BLX-5 droid, who was built for heavy-industrial work. He was activated at the Fondor shipyards and, by sheer luck from his point of view, did not have frequent memory wipes. All droids were supposed to be memory-wiped every so often, so that they did not acquire a personality and decide to rebel against their masters. As a result Bollux developed a complex personality, which became more complex as his systems were upgraded and structural modifications took place. In the service of the Rebellion, Bollux worked in the area of trenches and fortifications. He worked very hard, and also had an extremely pleasant personality. But as new-model droids were produced, Bollux inevitably became obsolete and was eventually sold off. This led to Bollux coming into the service of Doc, an outlaw tech who had an asteroid base in the corporate sector. He had a daughter, Jessa. Jessa used to upgrade Bollux's systems and indeed gave him the nickname of Bollux.
Blue Max, on the other hand, was a small droid. Just a cube in fact. He could not move of his own accord, but was very advanced and had more memory and systems than most of the new starship computers. Blue Max also came into the service of Doc, after he had been stolen from a Imperial base. Doc wanted a droid that contrasted with Bollux, as he wanted them to work together. Therefore he reprogrammed Blue Max with a perkier and obtrusive personality. He had several appendages, which included a red photoreceptor mounted where his head should have been. But these appendages did not allow Blue Max to move around, so Doc and Jessa placed Blue Max into Bollux's chest. From there, Bollux would be able to open his chest and gain knowledge from Blue Max. He could also remove the cube completely.
When Doc went missing, Jessa hired Han to find him. She insisted that Bollux and Blue Max go with Han, despite his dislike for having droids aboard his ship. It was lucky that they did go with him, as they helped him immensely with the mission. A mission that almost ended in disaster at Star's End, a penal facility on the planet Mytus VII. When Doc was found, Bollux decided that he wanted to stay with Han. By this time Bollux was a free droid, so he chose of his own accord. Blue Max tagged along, although he didn't really have that much choice in the matter. Both droids planned to return to Doc and Jesaa at some stage, but for now they wanted to see a bit more of the galaxy.
The droids helped Han out of many situations, including blackmail from a slaver called Zlarb. Zlarb was later caught by Corporate Sector Auditor General Fiolla, with the help of Han and, more so, of the two droids. Han probably would not have survived as long as he has without those two droids, but they were to part company when he decided to go back to the Outer Rim and into Imperial Territory. No-one knows where they went, or if they are still active.