Synaptic transmission in the cortex is characterized by the activity-dependent short-term plasticity (STP), which can be broadly classified as synaptic depression and synaptic facilitation. As recent experiments indicate, different cortical areas exhibit variable mixes of facilitation and depression, which are also specific for connections between different types of neurons. In the first half of my presentation, I will describe the basics of dynamic synaptic transmission, its biophysical underpinnings and the ways it can be captured in biophysically motivated phenomenological models. I will also discuss some immediate implications of STP on information transmission between ensembles of neocortical neurons. In the second half of the presentation, I will focus on the effects of STP on the dynamics of recurrent networks and resulting neural computation. I will introduce the 'population spikes' (PSs), which are brief epochs of highly ynchronized activity that emerge in recurrent networks with dominating synaptic depression between excitatory neurons. PSs can underlie some of the response properties of neurons in the auditory cortex. I will then describe the recently introduced idea that synaptic facilitation could be utilized in order to maintain information about the incoming stimuli in the facilitation level of recurrent connections between the targeted neurons, thus providing an effective mechanism for short-term memory for a period of several seconds after the termination of the stimulus.