One Factor

just use the short rate for everything

also called relative value
use observed market prices

assumes interest rate volatility is independent (not related to) the level of the interest rate

Ho and Lee (1986)
No mean reversion

Hull and White (HW) (1990)
This model extends the Vasicek Model and Cox-Ingersoll-Ross models and allows for mean reversion.

assumes interest rate volatility depends on the level of the interest rate

Black (1976)

Heath-Jarrow-Morton (HJM) (1987)

Black-Derman-Toy (BDT) (1990)
Allows for mean reversion which is determined by market conditions

Black-Karasinski (BK)
Allows for mean reversion

Kalotay-Williams-Fabozzi (KWF)
No mean reversion. For pricing bonds with embedded options

Vasicek (1977)

Brennan-Schwartz (1979, 1982)

Cox-Ingersoll-Rox (CIR) (1981, 1985)
This is a square root process