Blow-up and quenching phenomena for semilinear parabolic first initial-boundary value problems on a semi-infinite interval are studied. For the blow-up problem with a stationary source, it is shown that the problem has a unique solution u before a blow-up occurs, and if u blows up, then it blows up in a finite time at the single point b only. A criterion for u to blow up in a finite time and a criterion for u to exist globally are given. It is shown that there exists a critical position b* for the nonlinear source to be placed such that no blow-up occurs for b ≤ b*, and u blows up in a finite time for b > b*. The formula for computing b* is also derived. For the quenching problem with a stationary source, it has a unique continuous solution u before a quenching occurs, and u is a strictly increasing function of t for 0 < x < ∞. It is shown that if a quenching occurs, then u quenches in a finite time only at the point b. A criterion for u to exist globally and a criterion for u to quench in a finite time are given. It is also shown that there exists a critical position b* such that for b ≤ b*, u exists for 0 ≤ t < ∞, and for b > b*, u quenches in a finite time. This implies that u does not quench in infinite time. The formula for computing b* is also derived. For the quenching problem with a moving source, it is shown that the problem has a unique continuous solution u before a quenching occurs, and if u quenches in a finite time t q , then it occurs at x = vt q only. A criterion for u to exists globally and a criterion for u to quench in a finite time are given. The problem is shown to have a critical speed v* such that u quenches in a finite time for v < v* and u exists globally for v ≥ v*. This implies u does not quench in infinite time. The formula for computing v* is also derived.