LTE is the next-step of the evolution of UMTS (3G) and HSDPA (3.5G). It's the only wireless network technology that's correctly called 4G. Some carries may market their high-speed HSDPA+ networks as 4G, but that's not technically correct.
Some of the improvements LTE brings along over the currently used wireless mobile radio technologies are a better spectral efficiency, lower costs, higher transfer speeds, improved services, etc.
LTE networks are widely available in the USA by carriers such as AT&T, Sprint and Verizon. In Europe, the network standard is not as widely spread and have limited coverage.
Theoretically, LTE networks should provide wireless data downlink speeds of up to 300Mbps and uplink speeds of up to 75Mbps.
Originally, LTE was conceived as an IP-based wireless system used purely for carrying data traffic. Network carriers were supposed to provide voice communication via their concurrent 2G/3G networks or by using VoIP. By popular request however, Voice over LTE (VoLTE) was a standardised system for transferring voice traffic over LTE. Currently, the availability of Voice over LTE (VoLTE) depends on the carrier implementation.
Unfortunately, the current implementations of LTE use different frequency bands in different countries, making interoperability an issue. LTE networks throughout the world can be seen utilizing one or several different network bands such as:
Band 1, 2100MHz (Japan, Philippines, South Korea);
Band 3, 1800MHz (Australia, Belgium, Finland, Germany, Hong Kong, Hungary, Italy, Singapore, Slovenia, Slovakia, South Korea, United Arab Emirates, UK)
Band 4, 1700MHz (AT&T in the United States)
Band 7, 2600MHz (Austria, Brazil, Canada, Finland, Germany, Hong Kong, Russia, Singapore, Sweden, Switzerland)
Band 17, 700MHz (AT&T and Verizon in the United States, Canada)