Some recent progress on occupation times of stochastic process will be presented. We focus on the occupation times related the first exit time and the last exit time, and obtain some results. 1)Potential measures that are discounted by joint occupation times over semi-infinite intervals $(-\infty, 0)$ and $(0, +\infty)$ for spectrally negative L\'{e}vy processes(SNLP). 2) Laplace transforms of joint occupation times over disjoint intervals $(0,a) and (a,b)$ for (SNLP). 3)Occupation times over intervals $(a, r)$ and $(r, b)$ before it first exits from either $a$ or $b$ for diffusion processes. 4) Exit identities for diffusion processes observed at Poisson arrival times. 5) joint Laplace transforms on the occupation time of interval $[a, b]$ before the process $X$ exits from a larger interval $[c, d]$ and the associated exit time for diffusion processes. 6)Potential measures that are discounted by joint occupation times over semi-infinite intervals $(-\infty, a)$ and $(a, +\infty)$ for diffusion processes.

Occupation times related the last exit time is aiso hot issue. Some result will also be presented. 7)Joint Laplace transforms of the last exit time by their joint occupation times over semi-infinite intervals $(-\infty,0)$ and $(0,\infty)$. 8) Joint Laplace transforms of the last exit time from two semi-infinite interval, the value of the process, and the associated occupation time before exponential time. 9)Joint Laplace transforms of occupation time before noo-exponential time. 10)Joint distributions concerning last exit time for diffusion processes.