The Product Line
If there is a start, it was in 1965, when HP Labs in Palo Alto near San Francisco started with two completely different projects.
The 2116 Minicomputer
The 9100A Calculator
Both projects were practically independent of each other. Production of the 2116 was startet one year later in the HP's minicomputer division, located at Cupertino, California. Production of the 9100 began in 1968 in HP's Loveland Division in Colorado. The 9100 was a fairly sucessful product, however the architecture of the 9100, although ingenious for the time, was inadaquate for the necessary up-scaling towards larger memory capacities, versatile I/O and more flexible programming.

Timeline
When looking for a successor for the 9100, the desktop computer division in Colorado decided to back on the prooved processor design of the 2116 in order to develop a complete new family of desktop calculators, the 9800 series. Now the 2116 with its 16-bit architecture was a bit too heavy to be implemented in the case of a desktop calculator, so HP's R&D serialized the 16-bit architecture down to single-bit/single-digit processing, which required a much simpler design. However, compared to the 2116, not only the size, but also the performance decreased dramatically.
The 9830A
So both development lines, the minicomputer development and the desktop calculator development, met in HP's 9800 series of desktop calculators. And actually, the 9820 and 9830 already could be considered much more as desktop computers than calculators. The 9810 was introduced in 1971, and the 9820 and 9830 were introduced in 1972. They sold remarkably well, and HP decided to continue the line with another generation of desktop calculators, the 98x5 systems.
Although not really prooved, it seems obvious that there was some competition between HP and WANG Laboratories, which started by grabbing a large share of WANG's position in the market of desktop calculators with the introduction of the HP 9100. From now on, each time WANG tried to catch up with its calculators, HP was a bit faster and delivered an even better product. However, WANGs market strategy had a strong focus on real computers, and when the 2200 minicomputer was released in 1973 with its CRT display, its instant-on capabitilites and its fast BASIC performance (all the BASIC firmware was micro-coded!), HP had to make a significant step forward.
The 9815A Calculator

9825A and 9835A Desktop Systems
Whereas the 9815 was mostly a programmable calculator, the 9825 was intended as an instrument controller (and most 9825 systems sold were used exactly for that purpose). The 9835 used a CRT display instead of the LEDs, and was programmed in HP BASIC instead of HPL, but actually the 9835 did'nt have a real target group, since it was a bit too large and expensive for a plain instrument controller, and not as performant as the 9845 for serious computing applications. Both the 9825 and the 9835 used a single built-in cartridge tape drive as standard mass storage.
The 9845A
The 9845C
The 9845B was introduced in 1979/1980, and was mostly a redesign of the original 9845A, allowing a larger amount of read/write memory. According to Joe Rigdon the 9845B had the development code name "Galleon". The 9845C was introduced at the end of 1980 and provided sophisticated color graphics with hardware accelerated vector graphics and a light-pen as pointing device. The color monitor, which had an estimated 98% part on the innovations of the 9845C, had the development code name "Odyssey". In 1982 a bit-slice implementation of the language processor with the code name "Steamer" was offered, which was a replacment for the original LPU hybrid processor and was capable of executing time consuming BASIC instructions in microcode, which could accelerate the execution of BASIC programs up to a factor of seven.
The systems equipped with this new bit-slice processor were indicated as "option 200" models.In the 1985, HP claimed a combined worldwide installation base of 85,000 units for the 9825 and 9845 series.
The "9855A"
Although the 9845 desktop systems were full-fledged computers with a CPU based on the 2116 minicomputer architecture, they still had lots of design elements from the original 9100 calculator, like the BCD floating point arithmetics hardware and the instant-on ROM based system firmware.
The 9836
In 1982 the 500 series was launched, based on HP's first RISC CPU, the 32-bit FOCUS processor. The 500 series computers were introduced as "HP 9000" computers (shortly after the introduction, the 98x6 series was changed to include the "HP 9000" name). Although the series 200 were technically the first HP workstations which could be used with HP-UX (HP's own UNIX implementation) as operating system, the series 500 were the first models which were sold with this operating system. There were four different casings, the 9000/530 was a 19" rack-mount system, the 9000/540 was built into a mini-cabinet, the 9000/520 was the desktop variant and the 9000/550 already had the industrial design of the 300 series.
The 9000/520
All models contained a 10 MB hard disc drive. The model 520 desktop version also included a 5.25" floppy disc drive and could be alternatively used with HP Basic. The 500 series was designed for downward compatibility with the previous HP 200 series and the 9835/9845 systems and supported both the 9845 and the LIF file system in addition the newly developed Structured Directory Format (SDF). Many programs originally written for the 9835/9845 or 98x6 could be executed on the series 520 without change. One interesting fact ist that much of the OS (both HP-UX and Basic) was developed in parallel to the series 500 hardware design using an emulator running on an HP9845 with Assembly Execution and Development ROM.
The hardware architecture was a consequent improvement of the 9845 system in many aspects. Obviously the monitor design was re-used from the 9845 option 200 systems, however via a real look-up table, up to 16 colors out of 4096 could be displayed at once. The main advancements on the hardware side were the development of a new chipset (including the 32-bit CPU, an I/O processor, a memory control unit and a new DRAM chip with hardware error correction), a new way to produce high-density multi-layer PCB modules with surface mounted components (called "finistrates"), and the capability to operate up to three 32-bit processors in parallel (real multiprocessing). Due to the decision to pack everything still into one single desktop housing, the model 520 was the biggest and heaviest desktop system ever produced by HP (74 kg for the color system).
The workstations series was continued with the 300 series (1985), and, after the acquisition of the workstation manufacturer Apollo, the 400 series (1990) and 700 series (1991), all based on HP-UX.
There was a side line of microprocessor based personal computers, starting with the 80 series of BASIC computers in 1979, and continuing with the 100 series, which first introduced CP/M and then MS-DOS, and finally the Vectra family of IBM PC compatibles.