On November 17th, 2008, Intel released its Core i7-920 CPU with its proprietary performance-enhancing technology called Turbo Boost. It is technically the spiritual successor of Foxton (Enhanced Intel SpeedStep Technology), seeing as they both had similar purposes to fulfill. It could be also considered the direct successor of Intel's older (Dual) Dynamic Acceleration Technology, as both technologies would allow an active core to increase its speed if an inactive core was present.
This technology allows Intel's CPUs to increase their speed on-demand, given that the thermal design point and temperature limits have not been exceeded. If there is an on-die GPU integrated into the CPU's substrate or core, the GPU will also utilize Turbo Boost to increase its speed. However, the same limitations apply to the GPU as well.
Intel Turbo Boost Technology 1.0
First introduced in the 'Bloomfield' Core i7-9xx CPUs, it was meant to reduce the single-threaded disadvantage that plagued the older 2-core+ Intel CPUs. This was historically a big problem for those who were stuck with applications that couldn't recognize or fully utilize CPUs with more than 2 cores, leaving them with unsatisfactory performance. Note that this version of Turbo Boost was also implemented in 'Westmere-EX', 'Westmere-EP', 'Westmere-WS', 'Nehalem-EX', 'Nehalem-EP', 'Nehalem-WS', 'Gulftown', 'Beckton', 'Jasper Forest', 'Lynnfield', 'Clarksfield', 'Clarkdale', and 'Arrandale' architectures.
This version of Turbo Boost does not allow a Turbo Boost-enabled CPU to exceed its rated TDP (thermal design power/point), TDC (thermal design current), and TjMax (maximum junction temperature). If any of these limits are exceeded, Turbo Boost will disengage (it will not disable itself, it'll just turn inactive) and the CPU will slow itself down back to its base clock frequency. If the TjMax limit has been exceeded, the CPU will not clock itself back to its base clock frequency, but modulate at the lowest possible clock frequency to reduce heat as much as possible.
More importantly, this version does not have a 'turbo time limit' (also known as Tau by Intel's definition). This means that Turbo Boost will always engage, but only if the aforementioned limits have not been hit. All of the previously stated limits and characteristics will also apply to a Turbo-Boost enabled CPU that has an integrated GPU as well (the TDC variable is shared with the GPU, but the TDP and TjMax are not).
Intel Turbo Boost Technology 2.0
This was the second version of Turbo Boost, first seen in the Sandy Bridge microarchitecture. It is present in all recent Intel CPUs too, although some of them are accompanied with an additional technology called 'Intel Turbo Boost Max Technology 3.0'.
In this version of Turbo Boost, the 'turbo time limit' feature now exists and is generally predefined by the system's vendors (the turbo time limit varies, some are set short or long on purpose). Other than that, a swathe of changes has been made to Turbo Boost to make it more customizable for the vendors' benefit. Fortunately, Turbo Boost can also be customized by the user, but only if it is left mostly untouched. Most system vendors would generally leave them locked, due to the probable damage or malfunction that can be caused by user intervention.
The most notable change done to Turbo Boost, was its behavior. This is due to how it checks for more than just three factors to engage. While it now allows a CPU to exceed its rated TDP (TDP value is used for Power Limit 1, or PL1), it will not engage forever as the turbo time limit will set in and disengage Turbo Boost. Another factor is the CPU's Power Limit 2 value (or PL2), as this could potentially affect its Turbo Boost capabilities. Note that the turbo time limit dictates how long will the CPU stay below the PL2 value before downgrading back to the PL1 value. There are also several more power limits to keep Turbo Boost controlled, but these are generally not used: Power Limit 3 (PL3, introduced with the Broadwell microarchitecture), and Power Limit 4 (PL4, introduced with the Skylake microarchitecture).
As Turbo Boost also applies to GPUs, the modified behavior applies to them too. The main difference is that the GPU has separated variables which controls its turbo time limit and power limit; they are not shared with the CPU's turbo variables (e.g. modifying the CPU's PL1/PL2/PL3/PL4/Tau will have no effect on the on-die GPU's Turbo Boost behavior).
Intel Burst Performance Technology
There is not much information available for this particular technology. Although, it could be reasonably assumed as a lower-end version of Turbo Boost Technology 1.0 or 2.0, depending on the CPU that has implemented this technology.
This version appears to be heavily based off Turbo Boost Technology 1.0, and it seems to be available in only low-end Celeron-based or Pentium-based Bonnell, Saltwell, Silvermont, Airmont, Goldmont, and Tremont Atom microarchitectures. It also has no version identification, unlike Turbo Boost Technology 1.0 and 2.0.
Intel Turbo Boost Max Technology 3.0
This is not a replacement for Turbo Boost, as it does not change anything related to the current Turbo Boost Technology. It is simply an addition to the current Turbo Boost Technology.
This technology takes advantage of the CPU's cores that are capable of reaching higher clock frequencies, generally by increments of 1 or 2 multiplier steps up (100 or 200 MHz). Depending on the architecture, the amount of cores that can benefit from this technology can be either one core (Broadwell-E), or two cores (Skylake). So far, this has not been introduced in any mobile chip, although the recently introduced 10th generation CPUs are stated to come with this technology enabled.