Writing:
p1 = ParametricPlot[{t, t}, {t, -1, 1},
Epilog -> {PointSize[0.02], Point[{-1, -1}], Point[{1, 1}]}];
p2 = ParametricPlot[{1, t}, {t, 1, 2},
Epilog -> {PointSize[0.02], Point[{1, 1}], Point[{1, 2}]}];
Show[p1, p2, PlotRange -> All]
I get:
and I do not understand why only the first two points are plotted.
Thank you!

Show->Possible Issues? – Mariusz Iwaniuk Mar 10 '18 at 10:50Epilog -> {PointSize[0.02], Point[{-1, -1}], Point[{1, 1}]}gets applied. Better to putEpiloginShow[]instead:Show[p1, p2, Epilog -> {PointSize[0.02], Point[{{-1, -1}, {1, 1}, {1, 2}}]}, PlotRange -> All]– J. M.'s missing motivation Mar 10 '18 at 11:39