Control the layer of a ConstantLine or ConstantRegion
Here are several solutions covering several MATLAB releases.
R2024a or later: set the Layer property
Starting in R2024a, xline, yline, xregion, and yregion all support the ability to be placed behind or in front of objects in an axes using the Layer property. The default for ConstantRegion, the object produced by xregion and yregion, is to appear in the 'bottom' layer and the default for ConstantLine, the underlying object for xline and yline, is to appear in the 'top' layer.
plot(1:10, LineWidth=6);
x1 = xline(2,LineWidth=6,Alpha=1); % default: top
x2 = xline(3,LineWidth=6,Alpha=1,Layer='bottom');
x3 = xregion(4,5,FaceAlpha=1); % default: bottom
x4 = xregion(6,7,FaceALpha=1,Layer='top');
Before R2024a: Use the LimitsChangedFcn with a Line object
Before R2024a, the Layer property was not available. Instead, you can plot a regular line and use the LimitsChangedFcn to update the bounds of the line any time the axis limits change.
% Plot data
figure()
v = 1:20;
plot(v,v.^2,'-c','LineWidth',6)
ax = gca();
hold on
% Add x-line
x = 10;
xl = plot([x,x],ylim(ax), 'k--', 'LineWidth', 4);
% Add y-line
y = 100;
yl = plot(xlim(ax), [y, y], 'k--', 'LineWidth', 4);
% Send x and y lines to the bottom of the stack
uistack([xl,yl],'bottom')
% Update the x and y line bounds any time the axes limits change
ax.XAxis.LimitsChangedFcn = @(ruler,~)set(xl, 'YData', ylim(ancestor(ruler,'axes')));
ax.YAxis.LimitsChangedFcn = @(ruler,~)set(yl, 'XData', xlim(ancestor(ruler,'axes')));
Alternative workaround
Lastly, here's the original answer to this question that relys on undocumented features which could change at any time. Here's now to set the ConstantLine to the back of the uistack (Nov 2020). As @Yi-xiao Liu points out, this will not work in Live Scripts.
% Set up example
figure()
plot(magic(5),'LineWidth',5)
xh = xline(3,'LineWidth',8,'Alpha',1);
% Set ConstantLine to 'back'
% Temporarily disable the warning that appears when accessing
% the undocumented properties.
warnState = warning('off','MATLAB:structOnObject');
cleanupObj = onCleanup(@()warning(warnState));
Sxh = struct(xh); % Get undocumented properties (you'll get a warning)
clear('cleanupObj') % Trigger warning reset
Sxh.Edge.Layer = 'back'; % Set ConstantLine uistack
