Updated April 2023

With the current state of Syria and Libya, get between Egypt and Europe by either shipping/air freighting, or by ferry between Greece and Israel via Sinai.
The overland crossing to Sudan goes via Argeen but most still via Wadi Halfa. See below.
Detailed descriptions here and here.
Travel to the fascinating ‘Gilf Kebir‘ region is now so highly regulated it’s just about impossible.

Money
Egyptian pound exchange rates

Price of fuel
’80’ octane (very low-grade fuel, avoid it); 5.5 LE
95 7.75 LE
Diesel (‘Solar’) 5.5 LE
World fuel prices.

Costs Moderate, along with vehicle immigration fees and the carnet.

Useful languages
Arabic, English.

Visas
Visas are still issued at the border for overlanders. If you fly in get an e-visa.

Border formalities
With a vehicle border formalities are among the most protracted in Africa, if not the world; it can take many hours – or days if shipping in. Buy insurance and ‘rent’ number plates at the border – sounds simple but it won’t be quick. A carnet is still needed, though some claim a fee of $400 will work.
Last tourist crossing from Libya was early 2014; now, no chance. The only direct way to Egypt is to ship from Greece; otherwise ferry via Israel and Jordan (see below). See here.

Egypt–Sudan border
Two land borders now operate on the east and west side of the Nile: Wadi Halfa and Argeen. Wadi Halfa still requires a one-hour crossing of Lake Nasser between Abu Simbel and Qustul; Aswan to Argeen and into Sudan on the west side is easily done is a day. See here. Costs from 2018 for the Qustul ferry > Wadi Halfa crossing.
It’s said you can get a Sudan visa in Aswan in a few days, though possibly not if you’re an American or a Brit. Less risk to get them in Cairo same day.
8 El Sherbiny St,
Dokki
N 30° 02.4’  E31° 12.7′
2 photos, $100
30.032886, 31.208852

Overland via Israel
Terrorist activity in the Sinai may have closed access to Israel near Gaza but the Red Sea Egyptian border at Taba (near Eilat) is open. If not, most the ferry from Nuweiba to Aqaba, Jordan, and from there into Israel for a freight ferry from Haifa to Greece (you fly).
South Sinai is certainly open and safe enough at the time of this update and it seems now you can also reach Egypt via Turkey, Iraq and Jordan.

Fuel and water reserves must be massive and various permits are required to get off the tarmac. These can take months to acquire and must be done via an accredited travel agent. Then you must hire and provision for a soldier or even an armed patrol. So, the best way to see this area is with locally hired vehicles and drivers, were it even possible. There are a few agencies that specialise in the Gilf but at this update visiting the region seems to be so highly regulated it’s as good as closed to tourism, certainly beyond the White Desert south of Bahariya.

Desert pistes 
The monumental aggravation of getting into the country as well as Egypt’s spectacular ancient monuments overshadow the remote desert regions in the west. The Egyptian Sahara (‘Western Desert’) is not as easily explored as other Saharan countries, especially with the current restrictions.
Look at the Michelin map and you’ll find the country almost bare of desert tracks – for a hardcore Saharan this used to be part of the appeal. The landscapes and rock art of Jebel Uweinat and the Gilf Kebir plateau and the Great Sand Sea all add up to a fascinating tour of this rarely explored corner of the Sahara.
Sahara Overland II gave a good overview; see also the S-Files for other trip reports from around 2003–4.