Determine direction of friction on a block held stationary against a vertical wall A block of mass $m$ is pushed up against a wall and held stationary by a force $ F$ that makes an acute angle $\theta $ with the horizontal. 
May I know how to determine the direction of the static friction $f_s$? 
Friction exerted by wall on the block acts in the opposite direction of the impending motion (or motion) of the block relative to wall. In absence of $F$ and $f_s$, the object will move vertically downwards. ($F$ is required to keep the block in contact with the wall) So $f_s$ acts vertically upwards? Should we assume that the block can only move parallel to the wall?
Please advise on my doubts. Thank you. 
 A: Friction always opposes motion, so for example if the block is moving up the wall, the force of friction retards the motion and acts downward. If the block moves down, then the force of friction acts up. Basically, which ever way the block moves, the friction acts in the opposite direction. You pretty much said that yourself. 
You said in absence of a force F and the static frictional force, fs, the block moves down, true, due to mg, but then you have said fs acts vertically up? With out F to push the box against the wall, no fs can exist between the wall and box... I'm guessing you mean the second the force is removed? The block falls and while falling against the wall, the fs acts up? yes it would for a small time, until the friction is kinetic, fk, which also acts in the up direction opposite to the motion of the box.
A: Friction exerted by wall on the block acts in the opposite direction of the impending motion (or motion) of the block relative to wall.
Yep, that's your answer.
In absence of F and fs, the object will move vertically downwards. (F is required to keep the block in contact with the wall) So fs acts vertically upwards?
Why are you discarding F? F is holding the block on the wall. There will also be a reaction force, R, that stops the block moving through the wall and therefore will have magnitude equal to the horizontal component of F.
Should we assume that the block can only move to parallel to the wall?
This seems reasonable. solid object don't easily move through one another or bounce away without some extra force.
To get the answer construct a free body diagram with all you forces, excluding friction you should have F, R and gravity. You should see that the direction of friction depends on the angel and strength of F. 
A: There are four forces to consider:
1)  Gravity, acting downward
2)  The push from the person. You said an acute angle, but that could mean either upward or downward because there are two directions from the horizontal. In the end, the analysis procedure is the same (but the results aren't).
3)  The normal force of the wall on the block, acting perpendicular to the wall.
4)  Because there is a normal force, the possibility of friction.  You specify a stationary block, so it is static friction, and it will be parallel to the wall, either up or down.
Analyze the system with a static friction of zero (0). If you get an acceleration, $a_0$, for the block, the static friction will be opposite that (frictionless) acceleration and will be of magnitude $ma_0$.
The direction of friction is opposed to the sliding of surfaces across each other. This is not necessarily the direction an object is moving.
