Is std::vector copying the objects with a push_back?

Yes, std::vector<T>::push_back() creates a copy of the argument and stores it in the vector. If you want to store pointers to objects in your vector, create a std::vector<whatever*> instead of std::vector<whatever>.

However, you need to make sure that the objects referenced by the pointers remain valid while the vector holds a reference to them (smart pointers utilizing the RAII idiom solve the problem).

From C++11 onwards, all the standard containers (std::vector, std::map, etc) support move semantics, meaning that you can now pass rvalues to standard containers and avoid a copy:

// Example object class.
class object
{
private:
    int             m_val1;
    std::string     m_val2;

public:
    // Constructor for object class.
    object(int val1, std::string &&val2) :
        m_val1(val1),
        m_val2(std::move(val2))
    {

    }
};

std::vector<object> myList;

// #1 Copy into the vector.
object foo1(1, "foo");
myList.push_back(foo1);

// #2 Move into the vector (no copy).
object foo2(1024, "bar");
myList.push_back(std::move(foo2));

// #3 Move temporary into vector (no copy).
myList.push_back(object(453, "baz"));

// #4 Create instance of object directly inside the vector (no copy, no move).
myList.emplace_back(453, "qux");

Alternatively you can use various smart pointers to get mostly the same effect:

std::unique_ptr example

std::vector<std::unique_ptr<object>> myPtrList;

// #5a unique_ptr can only ever be moved.
auto pFoo = std::make_unique<object>(1, "foo");
myPtrList.push_back(std::move(pFoo));

// #5b unique_ptr can only ever be moved.
myPtrList.push_back(std::make_unique<object>(1, "foo"));

std::shared_ptr example

std::vector<std::shared_ptr<object>> objectPtrList2;

// #6 shared_ptr can be used to retain a copy of the pointer and update both the vector
// value and the local copy simultaneously.
auto pFooShared = std::make_shared<object>(1, "foo");
objectPtrList2.push_back(pFooShared);
// Pointer to object stored in the vector, but pFooShared is still valid.

Yes, std::vector stores copies. How should vector know what the expected life-times of your objects are?

If you want to transfer or share ownership of the objects use pointers, possibly smart pointers like shared_ptr (found in Boost or TR1) to ease resource management.