This specific category of computers existed primarily in the 1980s. Manufacturers included Casio, Hewlett-Packard, Sharp, Tandy/Radio Shack (Selling Casio and Sharp models under their own TRS line) and many more.
The programming language was usually BASIC, but some devices offered alternatives. For example the Casio PB-2000 could be programmed in Assembly, BASIC, C, and Lisp. and Fortran and Prolog cards were also developed for it. The latest Sharp pocket computer, the PC G850V (2001) is programmable in C, Basic, and Assembler.  An important feature of pocket computers was that all programming languages were available for the device itself, not downloaded from a cross-compiler on a larger computer.
Though not identical, in principle personal digital assistants, handheld PCs, and programmable calculators serve many of the same functions as the old pocket computers, generally with significantly more computing power in a package the same size or smaller. The main distinction is that more modern designs (with the exception of programmable calculators) usually do not have included programming ability and are usually set up to act as clients of a larger system rather than as self-contained environments of their own, whereas the early pocket computers had their own data storage and input/output facilities such as printers and tape drives (connecting to one or two tape recorders as with the desktop computers of the era) as well as external floppy and 2½ inch mini floppy drives, bar code readers, video interfaces which could be connected to a television set or monitor, and standard RS-232 interfaces which allowed for a means of connecting to a desktop computer as well as other peripherals such as general-purpose printers, plotters, bar-code readers, data loggers, and even modems. Several models of electric typewriters by Smith Corona, IBM, Royal, Olivetti, and others can be used as printers by any computer or device with the correct ports, cables, and set up software on the computer side.