The main features of HII regions expanding in spherical and disk-like clouds with density gradients are reviewed. The spherical cases assume power-law density stratifications, r~w, and the disk-like cases include exponential, gaussian, and sech2 distributions. For power-law profiles, there is a critical exponent, wcrit = 3/2, above which the ionization front cannot be “trapped” and the cloud becomes fully ionized. For clouds with w < 3/2, the radius of the ionized region grows as t4/(7-2w) and drives a shock front into the ambient neutral medium. For w = wcrit = 3/2 the shock wave cannot detach from the ionization front and the two move together with a constant speed equal to about 2ci, where ci is the sound speed in the ionized gas. For w > 3/2 the expansion corresponds to the “champagne phase”, and two regimes, fast and slow, are apparent: between 3/2 < w ≤ 3, the slow regime, the inner region drives a weak shock moving with almost constant velocity through the cloud, and for w > 3, the fast regime, the shock becomes strong and accelerates with time.

For the case of disk-like clouds, which are assumed cylindrically symmetric, the dimensions of the initial HII regions along each azimuthal angle, θ, are described in terms of the Strömgren radius for the midplane density, Ro, and the disk scale height, H. For yo = Rosin(θ)/H ≤ α (where α is a constant dependent on the assumed density distribution) the whole HII region is contained within the disk, and for yo > α a conical section of the disk becomes totally ionized. The critical azimuthal angle above which the HII region becomes unbounded is defined by θcrit =sin-1(αH/Ro). The expansion of initially unbounded HII regions (i.e. with yo > α) proceeds along the z-axis and, if the disk column density remains constant during the evolution, the ionization front eventually recedes from infinity to become trapped within the expanding disk. For clouds threaded by a B-field oriented parallel to the symmetry axis, as expected in magnetically dominated clouds, this effect can be very prominent. The expanding gas overtaken by the receding ionization front maintains its linear momentum after recombination and is transformed into a high-velocity neutral outflow. In the absence of magnetic fields, the trapping has only a short duration.