I present an introduction into the mechanisms of generation of spikes and bursts in neurons and in Hodgkin-Huxley-type neuronal models. Then I present a deterministic model that reproduces spiking and bursting behavior of known types of cortical neurons. The model combines the biologically plausibility of Hodgkin-Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons. Using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop PC. \vskip .1in \noindent MATLAB and C++ code, as well as pdf file of the paper are available at http://www.nsi.edu/users/izhikevich/publications/spikes.htm