The 25th Dynasty of Egypt are apparently a rather confusing period for Egyptologists It represent a fine example of the complexity of studying Egyptian history.  For example, the following table provides the king's list offered by a number of different authoritative sources: 

It should be noted that the authors of all these books are highly accredited Egyptologists.

Actually, there is a fair amount of consistency in the order of the lists, once the uninitiated to Egyptology understand that the names can appear with very different spellings.  But, for example, lets take a more detailed look at the reign given to just one of the kings.  Arbitrarily, we will look at Shabaka, who, for the most part, is considered the second ruler of the 25th Dynasty:

Note that, with the exception of Monarchs of the Nile, all give the same number of years for Shabaka's reign.  This is obviously because it is much easier for Egyptologists to determine the length of a rulers reign then it is for them to determine the exact dates of the reign.

More interesting, perhaps, it how they classify this dynasty in the overall history of Egypt.  This history is divided into major time periods, consisting of the Early Dynastic Period, Old Kingdom, First Intermediate Period, Middle Kingdom, Second Intermediate Period, New Kingdom, Third Intermediate Period, Late Period, and the Greco/Roman Period. However, some of the books even vary on these classical divisions.  But, for example, we find the following:

To make matters somewhat worse, though probably correct, most references overlap this dynasty with other periods.

Regardless of the problems, this is an interesting period in Egypt's history, as well as an example of an often reoccurring theme.  We see that when Egypt is weak, Nubia becomes strong, and when Egypt is strong, Nubia suffers. However, this is the first time that the ruled becomes the rulers.

Piye

Most references point to Piye as being the first ruler of the 25th Dynasty. Obviously, different references refer to him under different names.  We believe he ruled Kush (Nubia) from about 750 to 719 BC. Piankhi was his birth name. But in various references, we see his birth name referred to as Piankhy, Piye, Piy and Piyi.  However, some references point out that his true name was Piye, and that this was wrongly read as Piankhi. His Throne Name was Men-kheper-re, meaning "The Manifestation of Re Abides"). But this name too will vary, being also spelled Menkheperra. Of course, this king, as most others, had several other names which are not generally provided. 

Piye ascended the Nubian (Kushite) thrown (or at least its northern half) as the successor of Kashta, which explains why at least one reference refers to Kashta as the founder of the 25th Dynasty.  Kashta apparently had made some earlier advances into Egypt.  But it was Piye who, for the first time, consolidated the rulership of Nubia and Egypt.

From the earliest dynastic periods, Nubia was always a matter of conquest for the Egyptian pharaohs, and as such, much of Nubia was often under the control of Egypt.  At times, it was very much a part of Egypt, and the customs of Nubia were a reflection of those in at least Upper Egypt.  This perhaps explains Piye's seemingly strong emotional ties with Egypt, what he considered to be part of his motherland, even though he was not from Egypt proper.  

So at least towards the end of the Third Intermediate Period, when Egypt seems to have surrendered to chaos with four kings claiming rule within Egypt, as well as a number of local chieftains exercising control, particularly in the Delta, Piye decided to step in and fix Egypt's problems.

Kashta had a stele erected at the Elephantine Temple of Khnum (current day Aswan), but in the early ears of Piye's reign, he extended his rule to Thebes itself.  There, he had his sister, Amenirdis I, named as the successor of Shepenwepet I, who had the title, "God's Wife of Amun".  Shepenwepet I was the sister of Rudamun of the Theban 23rd Dynasty, and apparently both Rudamun and Piye were recognized at Thebes at the same time. After the death of Rudamun, the Theban royal line seems to have abandoned Thebes in favor of Hierakleopolis, where Peftjauawy-bast, the last king of his dynasty remained an ally of Piye.

Amenirdis I as Wife of Amun

Soon, Piye was given a reason to intervene further north.  Tefnakhte (a Lybian), the Prince of Western Egypt based in the Delta city of Sais extended his control south by taking the city of Memphis, as well as the old Middle Kingdom of Itj-tawy (Lisht).  At first, Piye merely checked Tefnakhte's movement south with a pair of naval battles in Middle Egypt, though he left the Saite rulers in control of the North.  

However, after spending New Years in Nubia, Piye returned to Thebes in time for the great Opet Festival, and subsequently set about taking the remainder of Egypt under his control. His troops moved north, capturing three towns, and killing one of Tefnakhte's sons in the process.  Soon, Piye attacked the city of Ashmunein which was ruled by Nimlot, once an ally of Piye.  Using wooden siege towers, the city fell after five months.

Further North, Hierakleopolis, ruled by Piye's loyal ally, King Peftjauawybast, had been threatened by Tefnakhte, but the capture of Nimlot relieved the pressure on Hierakleopolis, and soon Piye had control of every major center south of Memphis, as well as capturing another of Tefnakhte's sons. 

The only real obstacle left for Piye was Memphis, the ancient capital of Egypt.  While the city was heavily fortified and defended, as well as the water of the Nile protecting its walls, Piye was able to use the masts of boats and ships in the Memphite harbor to assault the city and scale the walls.  In very short order, Memphis too was bought under his control.  It is said that his first act was to protect the temple of Ptah, and then to go there himself to be anointed and to worship.

With the capture of Memphis, most of the Delta rulers soon yielded to the Kushite king.  One notable exception was Tefnakhte, who even went so far as to mount another, but unsuccessful campaign against Piye. Finally, he to submitted to Piye's rule of Egypt, taking an oath of loyalty.  

After conquering Egypt, Piye simply went home to Nubia, and to our knowledge, never again returned to Egypt. He is portrayed as a ruler who did not glory in the smiting of his adversaries, as did other kings, but rather preferred treaties and alliances. He left the rule of the country largely in the hands of his vassals, but recorded his victories on a stela (called the Victory Stela, now in the Egyptian Museum) at Napata. He left few monuments in Egypt, other than an expansion of the Temple of Amun at Thebes (current day Luxor). Later, Tefnakhte would again claim kingdom and as the founder of the 24th Dynasty, rule at least the western Delta.  However, later successors to Piye would consolidate their control over Egypt, at least for a time.

Upon Piye's death, he was buried at El-Kurru, where he erected a small pyramid resembling the tall, narrow structures that had been built above many private tombs of Egypt's New Kingdom.  

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