This talk reports some of our recent work on regime-switching

diffusions in which continuous dynamics and discrete events coexist.

One of the distinct features is the discrete events depend on the

diffusions. First, motivational examples arising from singular perturbed

Markovian systems, manufacturing, and financial engineering will be

mentioned.  Then we recall the notion of recurrence and regularity.

After necessary and sufficient conditions for recurrence are

provided, ergodicity will be examined, and stability will be studied.

We will also mention some of our recent work on numerical solutions

Of controlled switching diffusions.