<p>In this paper, we study blow-up criteria, blow-up rates, global existences and a priori estimates for solutions to nonlinear parabolic problems involving the fractional Laplacian. We provide certain criteria to determine when the blow-up occurs; and in the case it occurs, we obtain almost optimal blow-up rates. We present conditions for the existence of global solutions and derive uniform a priori bounds for such solutions.</p><p>Unlike parabolic equations involving the regular Laplacian, there have been very few such results for fractional parabolic problems. To circumvent the difficulty caused by the non-locality of the fractional Laplacian, we develop a direct method of blowing-up and re-scaling to derive the blow-up rate. As applications, we also obtain the blow-up rate for indefinite fractional parabolic equations. This new method is not only applicable to various nonlocal problems but also to local ones.</p>