In 1962 Ivan Sutherland's Sketchpad software was the most famous early computer graphics program, which ran on the screen built into the TX2 computer developed at MIT.

In 1970 I used a Teletype Model 33 terminal connected to a GE timesharing system to write and execute statistical analysis programs written in BASIC. Dartmouth (where BASIC was invented) and the Dartmouth Time-Sharing System (DTSS) were pioneers in this area.

The IBM 3270 (1972), block oriented terminal typically used IBM's Systems Network Architecture (SNA) to communicate with a System/370 or System/360 mainframes.
It had 80 columns and 24 lines, but could address individual locations on the screen. With a block mode connection the host will completely draw the screen, populating it with fields in which the required data may be entered. It had an advantage over character mode terminal on slow connections.

The Tektronix 4000 series graphics workstation (1972) was popular in the CAD (Computer Aided Design) market. It used raster graphics (same as today's monitors), replacing the more expensive vector graphics terminals used for graphical applications.
 

These "dumb" terminals just printed out your interaction on a continuous roll of paper.
CRTs (Cathode Ray tubes) became popular in the 70's replacing paper terminals and punched cards with video displays showing 24 lines of 80 characters each. Characters were the regular ASCII characters.
They could be connected to computers via private lines or dial-up modems.
CRT initially just replaced the paper with a screen.

But, they eventually got smarter. The DEC VT100 (1978) used the ANSI 3.64 protocol to allow computers to send escape sequences specifying scrolling regions, different character sizes (regular, compressed, double-wide, double-high-and-wide), smooth scrolling, and on-screen keyboard-driven setup rather than the knobs, DIP switches and jumpers, providing a more sophisticated interface.

Personal Computers:
As personal computers came out they soon added modems and terminal emulation software so they could also be used as terminals. In fact in large corporations PCs primary use was as a terminal evolving into client server architectures.

The Apple II (1977) supported a 280x192 pixel display with three video modes: a 40 X 24 uppercase-only black-and-white text display, a 40 X 48 16-color low-resolution display, and a 140 X 280 6-color.
The video output was a NTSC hack to display on a standard TV.

MIT's X Window system (1984) provides a set of graphic primitives allowing a terminal to have multiple windows each connected to a different server. It kind of reversed the model with one terminal serving as a host to multiple remote applications.

The first IBM personal computer (1981) had a Mono Graphics Adaptor that displayed 80 characters on 25 lines in character mode and 640×200 pixels in graphics mode. The The Color Graphics Adapter (CGA) was introduced later in '81 with the same resolution.
The Hercules graphics card (HGC) which came out in 1982 could display 720×350 pixels.

The Grid Compass Laptop (1982, $8,150) was one of the first laptpops.

The Radio Shack TRS-80 Model 100 (1983) a laptop sized PDA (Personal Digital Assistant) for $1,099 becomes the standard for field news/sports reporters story writing.
It had an 8 line x 40 character LCD with 240 by 64 pixel addressable graphics.

The first Apple Macintosh (1984) had a 9 inch black and white 512x342 bit display , establishing the desktop publishing standard of 72 PPI. It supported proportional fonts so the number of characters per line varied. A 10 point mono spaced font would display 85 characters by 30 lines.

The Video Graphics Array (VGA) display hardware first introduced with the IBM PS/2 line of computers in 1987, could address 640x480 pixels.

See Mobile Device History for laptop, PDA (Personal Digital Assistant), smartphone and tablet evolution.